الجبر الأمثلة

{(x - y)}^{12}

${(x - y)}^{12}$

خطوة 1

يمكن عرض مثلث باسكال على النحو التالي:

1

$1$

1 - 1

$1 - 1$

1 - 2 - 1

$1 - 2 - 1$

\dots

$\dots$

1 - 10 - 45 - 120 - 210 - 252 - 210 - 120 - 45 - 10 - 1

$1 - 10 - 45 - 120 - 210 - 252 - 210 - 120 - 45 - 10 - 1$

1 - 11 - 55 - 165 - 330 - 462 - 462 - 330 - 165 - 55 - 11 - 1

$1 - 11 - 55 - 165 - 330 - 462 - 462 - 330 - 165 - 55 - 11 - 1$

1 - 12 - 66 - 220 - 495 - 792 - 924 - 792 - 495 - 220 - 66 - 12 - 1

$1 - 12 - 66 - 220 - 495 - 792 - 924 - 792 - 495 - 220 - 66 - 12 - 1$

يمكن استخدام المثلث لحساب معاملات توسيع

{(a + b)}^{n}

${(a + b)}^{n}$ بأخذ الأُس

n

$n$ وجمع

1

$1$ . ستتوافق المعاملات مع الخط

n + 1

$n + 1$ في المثلث. وبالنسبة إلى

{(x - y)}^{12}

${(x - y)}^{12}$ ،

n = 12

$n = 12$ ، لذا ستتوافق معاملات التوسيع مع الخط

13

$13$ .

خطوة 2

التوسيع يتبع القاعدة

{(a + b)}^{n} = c_{0} a^{n} b^{0} + c_{1} a^{n - 1} b^{1} + c_{n - 1} a^{1} b^{n - 1} + c_{n} a^{0} b^{n}

${(a + b)}^{n} = c_{0} a^{n} b^{0} + c_{1} a^{n - 1} b^{1} + c_{n - 1} a^{1} b^{n - 1} + c_{n} a^{0} b^{n}$ . وتساوي قيم المعاملات، من المثلث،

1 - 12 - 66 - 220 - 495 - 792 - 924 - 792 - 495 - 220 - 66 - 12 - 1

$1 - 12 - 66 - 220 - 495 - 792 - 924 - 792 - 495 - 220 - 66 - 12 - 1$ .

1 a^{12} b^{0} + 12 a^{11} b + 66 a^{10} b^{2} + 220 a^{9} b^{3} + 495 a^{8} b^{4} + 792 a^{7} b^{5} + 924 a^{6} b^{6} + 792 a^{5} b^{7} + 495 a^{4} b^{8} + 220 a^{3} b^{9} + 66 a^{2} b^{10} + 12 a b^{11} + 1 a^{0} b^{12}

$1 a^{12} b^{0} + 12 a^{11} b + 66 a^{10} b^{2} + 220 a^{9} b^{3} + 495 a^{8} b^{4} + 792 a^{7} b^{5} + 924 a^{6} b^{6} + 792 a^{5} b^{7} + 495 a^{4} b^{8} + 220 a^{3} b^{9} + 66 a^{2} b^{10} + 12 a b^{11} + 1 a^{0} b^{12}$

خطوة 3

عوّض بالقيمتين الفعليتين لـ

a

$a$

x

$x$ و

b

$b$

- y

$- y$ في العبارة.

1 {(x)}^{12} {(- y)}^{0} + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$1 {(x)}^{12} {(- y)}^{0} + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4

بسّط كل حد.

انقر لعرض المزيد من الخطوات...

خطوة 4.1

اضرب

{(x)}^{12}

${(x)}^{12}$ في

1

$1$ .

{(x)}^{12} {(- y)}^{0} + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

${(x)}^{12} {(- y)}^{0} + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.2

طبّق قاعدة الضرب على

- y

$- y$ .

x^{12} ({(- 1)}^{0} y^{0}) + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} ({(- 1)}^{0} y^{0}) + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.3

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

{(- 1)}^{0} x^{12} y^{0} + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

${(- 1)}^{0} x^{12} y^{0} + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.4

أي شيء مرفوع إلى

0

$0$ هو

1

$1$ .

1 x^{12} y^{0} + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$1 x^{12} y^{0} + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.5

اضرب

x^{12}

$x^{12}$ في

1

$1$ .

x^{12} y^{0} + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} y^{0} + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.6

أي شيء مرفوع إلى

0

$0$ هو

1

$1$ .

x^{12} \cdot 1 + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} \cdot 1 + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.7

اضرب

x^{12}

$x^{12}$ في

1

$1$ .

x^{12} + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} + 12 {(x)}^{11} {(- y)}^{1} + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.8

بسّط.

x^{12} + 12 x^{11} (- y) + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} + 12 x^{11} (- y) + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.9

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

x^{12} + 12 \cdot - 1 x^{11} y + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} + 12 \cdot - 1 x^{11} y + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.10

اضرب

12

$12$ في

- 1

$- 1$ .

x^{12} - 12 x^{11} y + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 {(x)}^{10} {(- y)}^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.11

طبّق قاعدة الضرب على

- y

$- y$ .

x^{12} - 12 x^{11} y + 66 x^{10} ({(- 1)}^{2} y^{2}) + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} ({(- 1)}^{2} y^{2}) + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.12

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

x^{12} - 12 x^{11} y + 66 \cdot {(- 1)}^{2} x^{10} y^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 \cdot {(- 1)}^{2} x^{10} y^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.13

ارفع

- 1

$- 1$ إلى القوة

2

$2$ .

x^{12} - 12 x^{11} y + 66 \cdot 1 x^{10} y^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 \cdot 1 x^{10} y^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.14

اضرب

66

$66$ في

1

$1$ .

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} + 220 {(x)}^{9} {(- y)}^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.15

طبّق قاعدة الضرب على

- y

$- y$ .

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} + 220 x^{9} ({(- 1)}^{3} y^{3}) + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} + 220 x^{9} ({(- 1)}^{3} y^{3}) + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.16

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} + 220 \cdot {(- 1)}^{3} x^{9} y^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} + 220 \cdot {(- 1)}^{3} x^{9} y^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.17

ارفع

- 1

$- 1$ إلى القوة

3

$3$ .

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} + 220 \cdot - 1 x^{9} y^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} + 220 \cdot - 1 x^{9} y^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.18

اضرب

220

$220$ في

- 1

$- 1$ .

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 {(x)}^{8} {(- y)}^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.19

طبّق قاعدة الضرب على

- y

$- y$ .

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} ({(- 1)}^{4} y^{4}) + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} ({(- 1)}^{4} y^{4}) + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.20

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 \cdot {(- 1)}^{4} x^{8} y^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 \cdot {(- 1)}^{4} x^{8} y^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.21

ارفع

- 1

$- 1$ إلى القوة

4

$4$ .

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 \cdot 1 x^{8} y^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 \cdot 1 x^{8} y^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.22

اضرب

495

$495$ في

1

$1$ .

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} + 792 {(x)}^{7} {(- y)}^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.23

طبّق قاعدة الضرب على

- y

$- y$ .

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} + 792 x^{7} ({(- 1)}^{5} y^{5}) + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} + 792 x^{7} ({(- 1)}^{5} y^{5}) + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.24

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} + 792 \cdot {(- 1)}^{5} x^{7} y^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} + 792 \cdot {(- 1)}^{5} x^{7} y^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.25

ارفع

- 1

$- 1$ إلى القوة

5

$5$ .

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} + 792 \cdot - 1 x^{7} y^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} + 792 \cdot - 1 x^{7} y^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.26

اضرب

792

$792$ في

- 1

$- 1$ .

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 {(x)}^{6} {(- y)}^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.27

طبّق قاعدة الضرب على

- y

$- y$ .

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} ({(- 1)}^{6} y^{6}) + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} ({(- 1)}^{6} y^{6}) + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.28

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 \cdot {(- 1)}^{6} x^{6} y^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 \cdot {(- 1)}^{6} x^{6} y^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.29

ارفع

- 1

$- 1$ إلى القوة

6

$6$ .

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 \cdot 1 x^{6} y^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 \cdot 1 x^{6} y^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.30

اضرب

924

$924$ في

1

$1$ .

x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} + 792 {(x)}^{5} {(- y)}^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.31

طبّق قاعدة الضرب على

$- y$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} + 792 x^{5} ({(- 1)}^{7} y^{7}) + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.32

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} + 792 \cdot {(- 1)}^{7} x^{5} y^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.33

ارفع

$- 1$ إلى القوة

$7$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} + 792 \cdot - 1 x^{5} y^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.34

اضرب

$792$ في

$- 1$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 {(x)}^{4} {(- y)}^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.35

طبّق قاعدة الضرب على

$- y$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} ({(- 1)}^{8} y^{8}) + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.36

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 \cdot {(- 1)}^{8} x^{4} y^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.37

ارفع

$- 1$ إلى القوة

$8$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 \cdot 1 x^{4} y^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.38

اضرب

$495$ في

$1$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} y^{8} + 220 {(x)}^{3} {(- y)}^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.39

طبّق قاعدة الضرب على

$- y$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} y^{8} + 220 x^{3} ({(- 1)}^{9} y^{9}) + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.40

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} y^{8} + 220 \cdot {(- 1)}^{9} x^{3} y^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.41

ارفع

$- 1$ إلى القوة

$9$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} y^{8} + 220 \cdot - 1 x^{3} y^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.42

اضرب

$220$ في

$- 1$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} y^{8} - 220 x^{3} y^{9} + 66 {(x)}^{2} {(- y)}^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.43

طبّق قاعدة الضرب على

$- y$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} y^{8} - 220 x^{3} y^{9} + 66 x^{2} ({(- 1)}^{10} y^{10}) + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.44

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} y^{8} - 220 x^{3} y^{9} + 66 \cdot {(- 1)}^{10} x^{2} y^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.45

ارفع

$- 1$ إلى القوة

$10$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} y^{8} - 220 x^{3} y^{9} + 66 \cdot 1 x^{2} y^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.46

اضرب

$66$ في

$1$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} y^{8} - 220 x^{3} y^{9} + 66 x^{2} y^{10} + 12 {(x)}^{1} {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.47

بسّط.

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} y^{8} - 220 x^{3} y^{9} + 66 x^{2} y^{10} + 12 x {(- y)}^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.48

طبّق قاعدة الضرب على

$- y$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} y^{8} - 220 x^{3} y^{9} + 66 x^{2} y^{10} + 12 x ({(- 1)}^{11} y^{11}) + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.49

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} y^{8} - 220 x^{3} y^{9} + 66 x^{2} y^{10} + 12 \cdot {(- 1)}^{11} x y^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.50

ارفع

$- 1$ إلى القوة

$11$ .

خطوة 4.51

اضرب

$12$ في

$- 1$ .

$x^{12} - 12 x^{11} y + 66 x^{10} y^{2} - 220 x^{9} y^{3} + 495 x^{8} y^{4} - 792 x^{7} y^{5} + 924 x^{6} y^{6} - 792 x^{5} y^{7} + 495 x^{4} y^{8} - 220 x^{3} y^{9} + 66 x^{2} y^{10} - 12 x y^{11} + 1 {(x)}^{0} {(- y)}^{12}$

خطوة 4.52

اضرب

${(x)}^{0}$ في

$1$ .

خطوة 4.53

أي شيء مرفوع إلى

$0$ هو

$1$ .

خطوة 4.54

اضرب

${(- y)}^{12}$ في

$1$ .

خطوة 4.55

طبّق قاعدة الضرب على

$- y$ .

خطوة 4.56

ارفع

$- 1$ إلى القوة

$12$ .

خطوة 4.57

اضرب

$y^{12}$ في

$1$ .