حلول الأسئلة

السؤال

أوجد ناتج كل مما يأتي واكتبه في أبسط صورة.

الحل

table attributes columnalign right columnspacing 1em end attributes row cell left parenthesis 6 a squared plus 5 a plus 10 right parenthesis minus left parenthesis 4 a squared plus 6 a plus 12 right parenthesis end cell row cell 6 a squared plus 5 a plus 10 minus 4 a squared minus 6 a minus 12 end cell row cell 2 a squared minus a minus 2 end cell end table

شاهد حلول جميع الاسئلة

تمارين ومسائل

تمارين ومسائل

بسط كل مما يأتي مفترضاً أن أياً من المتغيرات لا يساوي الصفر.

14)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell left parenthesis 5 x cubed y to the power of negative 5 end exponent right parenthesis left parenthesis 4 x y cubed right parenthesis end cell row blank cell fraction numerator 20 x to the power of 4 over denominator y squared end fraction equals 20 x to the power of 4 y to the power of negative 2 end exponent end cell end table

15)

table attributes columnalign right columnspacing 1em end attributes row cell fraction numerator negative y cubed z to the power of 5 over denominator y squared z cubed end fraction end cell row cell negative y to the power of 3 minus 2 end exponent z to the power of 5 minus 3 end exponent equals end cell row cell negative y z squared equals end cell end table

16)

table attributes columnalign right columnspacing 1em end attributes row cell fraction numerator negative 7 x to the power of 5 y to the power of 5 z to the power of 4 over denominator 21 x to the power of 7 y to the power of 5 z squared end fraction end cell row cell fraction numerator negative 7 x to the power of 5 minus 7 end exponent y to the power of 5 minus 5 end exponent z to the power of 4 minus 2 end exponent over denominator 21 end fraction equals end cell row cell negative fraction numerator z squared over denominator 3 x squared end fraction equals end cell end table

17)

n to the power of 20 equals n to the power of 54 equals left parenthesis n to the power of 5 right parenthesis to the power of 4

حدد ما إذا كانت كل عبارة فيما يأتي كثيرة حدود أم لا وإذا كانت فاذكر درجتها.

18)

2 x squared minus 3 x plus 5

نعم , 2

19)

a cubed minus 11

نعم , 3

20)

fraction numerator 5 n p over denominator n squared end fraction minus fraction numerator 2 g over denominator 8 end fraction

21)

square root of m minus 7 end root

لا.

أوجد ناتج كل مما يأتي واكتبه في أبسط صورة.

22)

table attributes columnalign right columnspacing 1em end attributes row cell left parenthesis 6 a squared plus 5 a plus 10 right parenthesis minus left parenthesis 4 a squared plus 6 a plus 12 right parenthesis end cell row cell 6 a squared plus 5 a plus 10 minus 4 a squared minus 6 a minus 12 end cell row cell 2 a squared minus a minus 2 end cell end table

23)

table attributes columnalign right columnspacing 1em end attributes row cell 4 x left parenthesis 2 x squared plus y right parenthesis end cell row cell 8 x cubed plus 4 x y end cell end table

24)

table attributes columnalign right columnspacing 1em end attributes row cell left parenthesis x minus y right parenthesis left parenthesis x squared plus 2 x y plus y squared right parenthesis end cell row cell x cubed plus 2 x squared y plus x y squared minus x squared y minus 2 x y cubed minus y cubed end cell row cell x cubed plus x squared y minus x y squared minus y cubed end cell end table

25)

left parenthesis a plus b right parenthesis left parenthesis a cubed minus 3 a b minus b squared right parenthesis

26) مزرعة:

تكلفة تنسيق المزرعة = 200 x plus 150 left parenthesis 15 minus x right parenthesis

بالضرب في القوس وجمع العناصر المتشابهة table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell 12 x plus 2250 minus 150 x end cell row blank cell 50 x plus 2250 end cell end table

27)

table attributes columnspacing 1em end attributes row cell left parenthesis fraction numerator 8 x squared y cubed over denominator 24 x cubed y squared end fraction right parenthesis to the power of 4 end cell row cell fraction numerator 8 to the power of 4 x to the power of 24 y to the power of 34 over denominator 24 to the power of 4 x to the power of 34 y to the power of 24 end fraction equals end cell row cell fraction numerator x to the power of 8 y to the power of 12 over denominator 3 to the power of 4 x to the power of 12 y to the power of 8 end fraction equals end cell row cell fraction numerator y to the power of 4 over denominator 81 x to the power of 4 end fraction equals end cell end table

28)

table attributes columnspacing 1em end attributes row cell left parenthesis fraction numerator 4 x to the power of negative 2 end exponent y cubed over denominator x y to the power of negative 4 end exponent end fraction right parenthesis to the power of negative 2 end exponent end cell row cell fraction numerator 4 to the power of negative 2 end exponent x to the power of 4 y to the power of negative 6 end exponent over denominator x to the power of negative 2 end exponent y to the power of 8 end fraction equals end cell row cell fraction numerator x to the power of 6 over denominator 16 y to the power of 14 end fraction equals end cell end table

29)

table attributes columnspacing 1em end attributes row cell left parenthesis a squared b cubed right parenthesis left parenthesis a b right parenthesis to the power of negative 2 end exponent end cell row cell left parenthesis a squared b cubed right parenthesis left parenthesis a to the power of negative 2 end exponent b to the power of negative 2 end exponent right parenthesis equals end cell row cell b equals a to the power of 2 minus 2 end exponent b to the power of 3 minus 2 end exponent equals end cell end table

30)

table attributes columnalign right columnspacing 1em end attributes row cell left parenthesis negative 3 x cubed y right parenthesis squared left parenthesis 4 x y squared right parenthesis end cell row cell left parenthesis 9 x to the power of 6 y squared right parenthesis left parenthesis 4 x y squared right parenthesis equals end cell row cell 36 x to the power of 7 y to the power of 4 equals end cell end table

31)

table attributes columnalign right columnspacing 1em end attributes row cell fraction numerator 3 c squared d left parenthesis 2 c cubed d to the power of 5 right parenthesis over denominator 15 c to the power of 4 d squared end fraction end cell row cell fraction numerator 6 c to the power of 5 d to the power of 6 over denominator 15 c to the power of 4 d squared end fraction equals end cell row cell 2 over 5 c d to the power of 4 equals end cell end table

32)

table attributes columnalign right columnspacing 1em end attributes row cell 1 fourth g squared left parenthesis 8 g plus 12 h minus 16 g h squared right parenthesis end cell row cell 1 fourth g squared left parenthesis 8 g right parenthesis plus 1 fourth g squared left parenthesis 12 h right parenthesis minus 1 fourth g squared left parenthesis 16 g h squared right parenthesis equals end cell row cell 2 g cubed plus 3 g squared h minus 4 g cubed h squared equals end cell end table

33)

table attributes columnalign right columnspacing 1em end attributes row cell x to the power of negative 2 end exponent left parenthesis x to the power of 4 minus 3 x cubed plus x to the power of negative 1 end exponent right parenthesis end cell row cell x to the power of negative 2 end exponent left parenthesis x to the power of 4 right parenthesis minus x to the power of negative 2 end exponent left parenthesis 3 x cubed right parenthesis plus x to the power of negative 2 end exponent left parenthesis x to the power of negative 1 end exponent right parenthesis equals end cell row cell x squared minus 3 x plus 1 over x cubed equals end cell end table

34)

table attributes columnalign right columnspacing 1em end attributes row cell a to the power of negative 3 end exponent b squared left parenthesis b a cubed plus b to the power of negative 1 end exponent a squared plus b to the power of negative 2 end exponent a right parenthesis end cell row cell a to the power of negative 3 end exponent b squared left parenthesis b a cubed right parenthesis plus a to the power of negative 3 end exponent b squared left parenthesis b to the power of negative 1 end exponent a squared right parenthesis plus a to the power of negative 3 end exponent b squared left parenthesis b to the power of negative 2 end exponent a right parenthesis equals end cell row cell b cubed plus b over a plus 1 over a squared equals end cell end table

35)

table attributes columnalign right columnspacing 1em end attributes row cell left parenthesis n squared minus 7 right parenthesis left parenthesis 2 n cubed plus 4 right parenthesis end cell row cell n squared left parenthesis 2 n cubed right parenthesis plus n squared left parenthesis 4 right parenthesis minus 7 left parenthesis 2 n cubed right parenthesis minus 7 left parenthesis 4 right parenthesis equals end cell row cell 2 n to the power of 5 plus 4 n squared minus 14 n cubed minus 28 equals end cell row cell 2 n to the power of 5 minus 14 n cubed plus 4 n squared minus 28 equals end cell end table

36)

table attributes columnalign right columnspacing 1em end attributes row cell left parenthesis 2 x minus 2 y right parenthesis left parenthesis 4 x squared minus 8 x y plus 4 y squared right parenthesis equals end cell row cell 8 x cubed minus 16 x squared y plus 8 x y squared minus 8 x squared y plus 16 x y squared minus 8 y cubed equals end cell row cell 8 x cubed minus 24 x squared y plus 24 x y squared minus 8 y cubed equals end cell end table

37) فلك: ارجع إلى فقرة "لماذا" في بداية هذا الدرس.

a) ما الوقت الذي يستغرقه الضوء حتى يصل من المجرة المذكورة إلى الأرض؟

table attributes columnspacing 1em end attributes row cell fraction numerator 2.367 cross times 10 to the power of 21 over denominator 3 cross times 10 to the power of 8 end fraction equals end cell row cell fraction numerator 2.367 cross times 10 to the power of 21 minus 8 end exponent over denominator 3 end fraction equals end cell row cell fraction numerator 2.367 cross times 10 to the power of 13 over denominator 3 end fraction equals end cell row cell 0.789 cross times 10 to the power of 13 equals end cell row cell text = end text 7.89 cross times 10 to the power of 12 equals end cell end table

نحول الثواني إلى سنوات بالقسمة على 365*24*60*60

table attributes columnalign right columnspacing 1em end attributes row cell fraction numerator 7.890000000000 over denominator 60 cross times 60 cross times 24 cross times 365 end fraction equals end cell row cell space of 1em 250190.26 almost equal to end cell end table سنة

b) ما الوقت الذي يستغرقه الضوء حتى يصل من الشمس إلى المريخ إذا كانت المسافة بينهما 2.28 cross times 10 to the power of 11 straight m؟

table attributes columnspacing 1em end attributes row cell fraction numerator 2.28 cross times 10 to the power of 11 over denominator 3 cross times 10 to the power of 8 end fraction equals end cell row cell fraction numerator 2.28 cross times 10 to the power of 11 minus 8 end exponent over denominator 3 end fraction equals end cell end table

table attributes columnspacing 1em end attributes row cell fraction numerator 2.28 cross times 10 cubed over denominator 3 end fraction equals end cell row cell 0.76 cross times 10 cubed equals end cell row cell 760 equals 0.76 cross times 1000 equals end cell end table

ثانية ليصل الضوء من الشمس إلى المريخ نحول إلى دقائق بالقسمة على 60

الوقت = 12.67 almost equal to 760 over 60 دقيقة.

38) إذا كان 5 to the power of k plus 7 end exponent equals 5 to the power of 2 k minus 3 end exponent فما قيمة k؟

بما أن الأساس متساوي في الطرفين إذاً الأسس متساوية.

table attributes columnspacing 1em end attributes row cell k plus 7 equals 2 k minus 3 end cell row cell k equals 10 end cell end table

39) ما قيمة k التي تجعل q to the power of 41 equals q to the power of 4 k end exponent times q to the power of 5 صحيحة؟

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell q to the power of 41 equals q to the power of 4 k end exponent times q to the power of 5 end cell row blank cell q to the power of 41 equals q to the power of 4 k plus 5 end exponent end cell end table

بما أن الأساس متساوي في الطرفين إذاً الأسس متساوية.

table attributes columnalign right columnspacing 1em end attributes row cell 41 equals 4 k plus 5 end cell row cell 41 minus 5 equals 4 k end cell row cell 9 equals k end cell end table

40) تمثيلات متعددة: استعمل النموذج المجاور الذي يمثل حاصل ضرب 3 + x في 4 + x.

نموذج الضرب

a) هندسياً:

مساحة المستطيل = x squared plus 7 x plus 12

b) جبرياً:

مساحة المستطيل = left parenthesis x plus 4 right parenthesis left parenthesis x plus 3 right parenthesis

table attributes columnalign right columnspacing 1em end attributes row cell x squared plus 3 x plus 4 x plus 12 equals end cell row cell x squared plus 7 x plus 12 equals end cell end table

c) لفظياً:

مثل كل حد في المستطيل أو أكثر بحيث تمثل المساحة في النموذج ناتج حاصل الضرب.

مشاركة الدرس

السؤال

أوجد ناتج كل مما يأتي واكتبه في أبسط صورة.

الحل

table attributes columnalign right columnspacing 1em end attributes row cell left parenthesis 6 a squared plus 5 a plus 10 right parenthesis minus left parenthesis 4 a squared plus 6 a plus 12 right parenthesis end cell row cell 6 a squared plus 5 a plus 10 minus 4 a squared minus 6 a minus 12 end cell row cell 2 a squared minus a minus 2 end cell end table

تمارين ومسائل

تمارين ومسائل

بسط كل مما يأتي مفترضاً أن أياً من المتغيرات لا يساوي الصفر.

14)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell left parenthesis 5 x cubed y to the power of negative 5 end exponent right parenthesis left parenthesis 4 x y cubed right parenthesis end cell row blank cell fraction numerator 20 x to the power of 4 over denominator y squared end fraction equals 20 x to the power of 4 y to the power of negative 2 end exponent end cell end table

15)

table attributes columnalign right columnspacing 1em end attributes row cell fraction numerator negative y cubed z to the power of 5 over denominator y squared z cubed end fraction end cell row cell negative y to the power of 3 minus 2 end exponent z to the power of 5 minus 3 end exponent equals end cell row cell negative y z squared equals end cell end table

16)

table attributes columnalign right columnspacing 1em end attributes row cell fraction numerator negative 7 x to the power of 5 y to the power of 5 z to the power of 4 over denominator 21 x to the power of 7 y to the power of 5 z squared end fraction end cell row cell fraction numerator negative 7 x to the power of 5 minus 7 end exponent y to the power of 5 minus 5 end exponent z to the power of 4 minus 2 end exponent over denominator 21 end fraction equals end cell row cell negative fraction numerator z squared over denominator 3 x squared end fraction equals end cell end table

17)

n to the power of 20 equals n to the power of 54 equals left parenthesis n to the power of 5 right parenthesis to the power of 4

حدد ما إذا كانت كل عبارة فيما يأتي كثيرة حدود أم لا وإذا كانت فاذكر درجتها.

18)

2 x squared minus 3 x plus 5

نعم , 2

19)

a cubed minus 11

نعم , 3

20)

fraction numerator 5 n p over denominator n squared end fraction minus fraction numerator 2 g over denominator 8 end fraction

21)

square root of m minus 7 end root

لا.

أوجد ناتج كل مما يأتي واكتبه في أبسط صورة.

22)

table attributes columnalign right columnspacing 1em end attributes row cell left parenthesis 6 a squared plus 5 a plus 10 right parenthesis minus left parenthesis 4 a squared plus 6 a plus 12 right parenthesis end cell row cell 6 a squared plus 5 a plus 10 minus 4 a squared minus 6 a minus 12 end cell row cell 2 a squared minus a minus 2 end cell end table

23)

table attributes columnalign right columnspacing 1em end attributes row cell 4 x left parenthesis 2 x squared plus y right parenthesis end cell row cell 8 x cubed plus 4 x y end cell end table

24)

table attributes columnalign right columnspacing 1em end attributes row cell left parenthesis x minus y right parenthesis left parenthesis x squared plus 2 x y plus y squared right parenthesis end cell row cell x cubed plus 2 x squared y plus x y squared minus x squared y minus 2 x y cubed minus y cubed end cell row cell x cubed plus x squared y minus x y squared minus y cubed end cell end table

25)

left parenthesis a plus b right parenthesis left parenthesis a cubed minus 3 a b minus b squared right parenthesis

26) مزرعة:

تكلفة تنسيق المزرعة = 200 x plus 150 left parenthesis 15 minus x right parenthesis

بالضرب في القوس وجمع العناصر المتشابهة table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell 12 x plus 2250 minus 150 x end cell row blank cell 50 x plus 2250 end cell end table

27)

table attributes columnspacing 1em end attributes row cell left parenthesis fraction numerator 8 x squared y cubed over denominator 24 x cubed y squared end fraction right parenthesis to the power of 4 end cell row cell fraction numerator 8 to the power of 4 x to the power of 24 y to the power of 34 over denominator 24 to the power of 4 x to the power of 34 y to the power of 24 end fraction equals end cell row cell fraction numerator x to the power of 8 y to the power of 12 over denominator 3 to the power of 4 x to the power of 12 y to the power of 8 end fraction equals end cell row cell fraction numerator y to the power of 4 over denominator 81 x to the power of 4 end fraction equals end cell end table

28)

table attributes columnspacing 1em end attributes row cell left parenthesis fraction numerator 4 x to the power of negative 2 end exponent y cubed over denominator x y to the power of negative 4 end exponent end fraction right parenthesis to the power of negative 2 end exponent end cell row cell fraction numerator 4 to the power of negative 2 end exponent x to the power of 4 y to the power of negative 6 end exponent over denominator x to the power of negative 2 end exponent y to the power of 8 end fraction equals end cell row cell fraction numerator x to the power of 6 over denominator 16 y to the power of 14 end fraction equals end cell end table

29)

table attributes columnspacing 1em end attributes row cell left parenthesis a squared b cubed right parenthesis left parenthesis a b right parenthesis to the power of negative 2 end exponent end cell row cell left parenthesis a squared b cubed right parenthesis left parenthesis a to the power of negative 2 end exponent b to the power of negative 2 end exponent right parenthesis equals end cell row cell b equals a to the power of 2 minus 2 end exponent b to the power of 3 minus 2 end exponent equals end cell end table

30)

table attributes columnalign right columnspacing 1em end attributes row cell left parenthesis negative 3 x cubed y right parenthesis squared left parenthesis 4 x y squared right parenthesis end cell row cell left parenthesis 9 x to the power of 6 y squared right parenthesis left parenthesis 4 x y squared right parenthesis equals end cell row cell 36 x to the power of 7 y to the power of 4 equals end cell end table

31)

table attributes columnalign right columnspacing 1em end attributes row cell fraction numerator 3 c squared d left parenthesis 2 c cubed d to the power of 5 right parenthesis over denominator 15 c to the power of 4 d squared end fraction end cell row cell fraction numerator 6 c to the power of 5 d to the power of 6 over denominator 15 c to the power of 4 d squared end fraction equals end cell row cell 2 over 5 c d to the power of 4 equals end cell end table

32)

table attributes columnalign right columnspacing 1em end attributes row cell 1 fourth g squared left parenthesis 8 g plus 12 h minus 16 g h squared right parenthesis end cell row cell 1 fourth g squared left parenthesis 8 g right parenthesis plus 1 fourth g squared left parenthesis 12 h right parenthesis minus 1 fourth g squared left parenthesis 16 g h squared right parenthesis equals end cell row cell 2 g cubed plus 3 g squared h minus 4 g cubed h squared equals end cell end table

33)

table attributes columnalign right columnspacing 1em end attributes row cell x to the power of negative 2 end exponent left parenthesis x to the power of 4 minus 3 x cubed plus x to the power of negative 1 end exponent right parenthesis end cell row cell x to the power of negative 2 end exponent left parenthesis x to the power of 4 right parenthesis minus x to the power of negative 2 end exponent left parenthesis 3 x cubed right parenthesis plus x to the power of negative 2 end exponent left parenthesis x to the power of negative 1 end exponent right parenthesis equals end cell row cell x squared minus 3 x plus 1 over x cubed equals end cell end table

34)

table attributes columnalign right columnspacing 1em end attributes row cell a to the power of negative 3 end exponent b squared left parenthesis b a cubed plus b to the power of negative 1 end exponent a squared plus b to the power of negative 2 end exponent a right parenthesis end cell row cell a to the power of negative 3 end exponent b squared left parenthesis b a cubed right parenthesis plus a to the power of negative 3 end exponent b squared left parenthesis b to the power of negative 1 end exponent a squared right parenthesis plus a to the power of negative 3 end exponent b squared left parenthesis b to the power of negative 2 end exponent a right parenthesis equals end cell row cell b cubed plus b over a plus 1 over a squared equals end cell end table

35)

table attributes columnalign right columnspacing 1em end attributes row cell left parenthesis n squared minus 7 right parenthesis left parenthesis 2 n cubed plus 4 right parenthesis end cell row cell n squared left parenthesis 2 n cubed right parenthesis plus n squared left parenthesis 4 right parenthesis minus 7 left parenthesis 2 n cubed right parenthesis minus 7 left parenthesis 4 right parenthesis equals end cell row cell 2 n to the power of 5 plus 4 n squared minus 14 n cubed minus 28 equals end cell row cell 2 n to the power of 5 minus 14 n cubed plus 4 n squared minus 28 equals end cell end table

36)

table attributes columnalign right columnspacing 1em end attributes row cell left parenthesis 2 x minus 2 y right parenthesis left parenthesis 4 x squared minus 8 x y plus 4 y squared right parenthesis equals end cell row cell 8 x cubed minus 16 x squared y plus 8 x y squared minus 8 x squared y plus 16 x y squared minus 8 y cubed equals end cell row cell 8 x cubed minus 24 x squared y plus 24 x y squared minus 8 y cubed equals end cell end table

37) فلك: ارجع إلى فقرة "لماذا" في بداية هذا الدرس.

a) ما الوقت الذي يستغرقه الضوء حتى يصل من المجرة المذكورة إلى الأرض؟

table attributes columnspacing 1em end attributes row cell fraction numerator 2.367 cross times 10 to the power of 21 over denominator 3 cross times 10 to the power of 8 end fraction equals end cell row cell fraction numerator 2.367 cross times 10 to the power of 21 minus 8 end exponent over denominator 3 end fraction equals end cell row cell fraction numerator 2.367 cross times 10 to the power of 13 over denominator 3 end fraction equals end cell row cell 0.789 cross times 10 to the power of 13 equals end cell row cell text = end text 7.89 cross times 10 to the power of 12 equals end cell end table

نحول الثواني إلى سنوات بالقسمة على 365*24*60*60

table attributes columnalign right columnspacing 1em end attributes row cell fraction numerator 7.890000000000 over denominator 60 cross times 60 cross times 24 cross times 365 end fraction equals end cell row cell space of 1em 250190.26 almost equal to end cell end table سنة

b) ما الوقت الذي يستغرقه الضوء حتى يصل من الشمس إلى المريخ إذا كانت المسافة بينهما 2.28 cross times 10 to the power of 11 straight m؟

table attributes columnspacing 1em end attributes row cell fraction numerator 2.28 cross times 10 to the power of 11 over denominator 3 cross times 10 to the power of 8 end fraction equals end cell row cell fraction numerator 2.28 cross times 10 to the power of 11 minus 8 end exponent over denominator 3 end fraction equals end cell end table

table attributes columnspacing 1em end attributes row cell fraction numerator 2.28 cross times 10 cubed over denominator 3 end fraction equals end cell row cell 0.76 cross times 10 cubed equals end cell row cell 760 equals 0.76 cross times 1000 equals end cell end table

ثانية ليصل الضوء من الشمس إلى المريخ نحول إلى دقائق بالقسمة على 60

الوقت = 12.67 almost equal to 760 over 60 دقيقة.

38) إذا كان 5 to the power of k plus 7 end exponent equals 5 to the power of 2 k minus 3 end exponent فما قيمة k؟

بما أن الأساس متساوي في الطرفين إذاً الأسس متساوية.

table attributes columnspacing 1em end attributes row cell k plus 7 equals 2 k minus 3 end cell row cell k equals 10 end cell end table

39) ما قيمة k التي تجعل q to the power of 41 equals q to the power of 4 k end exponent times q to the power of 5 صحيحة؟

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell q to the power of 41 equals q to the power of 4 k end exponent times q to the power of 5 end cell row blank cell q to the power of 41 equals q to the power of 4 k plus 5 end exponent end cell end table

بما أن الأساس متساوي في الطرفين إذاً الأسس متساوية.

table attributes columnalign right columnspacing 1em end attributes row cell 41 equals 4 k plus 5 end cell row cell 41 minus 5 equals 4 k end cell row cell 9 equals k end cell end table

40) تمثيلات متعددة: استعمل النموذج المجاور الذي يمثل حاصل ضرب 3 + x في 4 + x.

نموذج الضرب

a) هندسياً:

مساحة المستطيل = x squared plus 7 x plus 12

b) جبرياً:

مساحة المستطيل = left parenthesis x plus 4 right parenthesis left parenthesis x plus 3 right parenthesis

table attributes columnalign right columnspacing 1em end attributes row cell x squared plus 3 x plus 4 x plus 12 equals end cell row cell x squared plus 7 x plus 12 equals end cell end table

c) لفظياً:

مثل كل حد في المستطيل أو أكثر بحيث تمثل المساحة في النموذج ناتج حاصل الضرب.