Prakalkulus Contoh

${(x - y)}^{11}$

Langkah 1

Segitiga Pascal dapat ditampilkan sebagai berikut:

$1$

$1 - 1$

$1 - 2 - 1$

$\dots$

$1 - 9 - 36 - 84 - 126 - 126 - 84 - 36 - 9 - 1$

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

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

Segitiganya dapat digunakan untuk menghitung koefisien dari perluasan ${(a + b)}^{n}$ dengan mengambil pangkat $n$ dan menambahkan $1$ . Koefisien akan sesuai dengan garis $n + 1$ dari segitiga. Untuk ${(x - y)}^{11}$ $n = 11$ sehingga koefisien dari perluasan akan sesuai dengan garis $12$ .

Langkah 2

Perluasan mengikuti aturan ${(a + b)}^{n} = c_{0} a^{n} b^{0} + c_{1} a^{n - 1} b^{1} + c_{n - 1} a^{1} b^{n - 1} + c_{n} a^{0} b^{n}$ . Nilai-nilai koefisien, dari segitiga, adalah $1 - 11 - 55 - 165 - 330 - 462 - 462 - 330 - 165 - 55 - 11 - 1$ .

$1 a^{11} b^{0} + 11 a^{10} b + 55 a^{9} b^{2} + 165 a^{8} b^{3} + 330 a^{7} b^{4} + 462 a^{6} b^{5} + 462 a^{5} b^{6} + 330 a^{4} b^{7} + 165 a^{3} b^{8} + 55 a^{2} b^{9} + 11 a b^{10} + 1 a^{0} b^{11}$

Langkah 3

Substitusikan nilai-nilai aktual dari $a$ $x$ dan $b$ $- y$ ke dalam pernyataannya.

$1 {(x)}^{11} {(- y)}^{0} + 11 {(x)}^{10} {(- y)}^{1} + 55 {(x)}^{9} {(- y)}^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 4.1

Kalikan ${(x)}^{11}$ dengan $1$ .

${(x)}^{11} {(- y)}^{0} + 11 {(x)}^{10} {(- y)}^{1} + 55 {(x)}^{9} {(- y)}^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.2

Terapkan kaidah hasil kali ke $- y$ .

$x^{11} ({(- 1)}^{0} y^{0}) + 11 {(x)}^{10} {(- y)}^{1} + 55 {(x)}^{9} {(- y)}^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.3

Tulis kembali menggunakan sifat komutatif dari perkalian.

${(- 1)}^{0} x^{11} y^{0} + 11 {(x)}^{10} {(- y)}^{1} + 55 {(x)}^{9} {(- y)}^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.4

Apa pun yang dinaikkan ke $0$ adalah $1$ .

$1 x^{11} y^{0} + 11 {(x)}^{10} {(- y)}^{1} + 55 {(x)}^{9} {(- y)}^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.5

Kalikan $x^{11}$ dengan $1$ .

$x^{11} y^{0} + 11 {(x)}^{10} {(- y)}^{1} + 55 {(x)}^{9} {(- y)}^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.6

Apa pun yang dinaikkan ke $0$ adalah $1$ .

$x^{11} \cdot 1 + 11 {(x)}^{10} {(- y)}^{1} + 55 {(x)}^{9} {(- y)}^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.7

Kalikan $x^{11}$ dengan $1$ .

$x^{11} + 11 {(x)}^{10} {(- y)}^{1} + 55 {(x)}^{9} {(- y)}^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.8

Sederhanakan.

$x^{11} + 11 x^{10} (- y) + 55 {(x)}^{9} {(- y)}^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.9

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{11} + 11 \cdot - 1 x^{10} y + 55 {(x)}^{9} {(- y)}^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.10

Kalikan $11$ dengan $- 1$ .

$x^{11} - 11 x^{10} y + 55 {(x)}^{9} {(- y)}^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.11

Terapkan kaidah hasil kali ke $- y$ .

$x^{11} - 11 x^{10} y + 55 x^{9} ({(- 1)}^{2} y^{2}) + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.12

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{11} - 11 x^{10} y + 55 \cdot {(- 1)}^{2} x^{9} y^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.13

Naikkan $- 1$ menjadi pangkat $2$ .

$x^{11} - 11 x^{10} y + 55 \cdot 1 x^{9} y^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.14

Kalikan $55$ dengan $1$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} + 165 {(x)}^{8} {(- y)}^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.15

Terapkan kaidah hasil kali ke $- y$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} + 165 x^{8} ({(- 1)}^{3} y^{3}) + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.16

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} + 165 \cdot {(- 1)}^{3} x^{8} y^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.17

Naikkan $- 1$ menjadi pangkat $3$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} + 165 \cdot - 1 x^{8} y^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.18

Kalikan $165$ dengan $- 1$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 {(x)}^{7} {(- y)}^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.19

Terapkan kaidah hasil kali ke $- y$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} ({(- 1)}^{4} y^{4}) + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.20

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 \cdot {(- 1)}^{4} x^{7} y^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.21

Naikkan $- 1$ menjadi pangkat $4$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 \cdot 1 x^{7} y^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.22

Kalikan $330$ dengan $1$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} + 462 {(x)}^{6} {(- y)}^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.23

Terapkan kaidah hasil kali ke $- y$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} + 462 x^{6} ({(- 1)}^{5} y^{5}) + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.24

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} + 462 \cdot {(- 1)}^{5} x^{6} y^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.25

Naikkan $- 1$ menjadi pangkat $5$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} + 462 \cdot - 1 x^{6} y^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.26

Kalikan $462$ dengan $- 1$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 {(x)}^{5} {(- y)}^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.27

Terapkan kaidah hasil kali ke $- y$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} ({(- 1)}^{6} y^{6}) + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.28

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 \cdot {(- 1)}^{6} x^{5} y^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.29

Naikkan $- 1$ menjadi pangkat $6$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 \cdot 1 x^{5} y^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.30

Kalikan $462$ dengan $1$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} + 330 {(x)}^{4} {(- y)}^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.31

Terapkan kaidah hasil kali ke $- y$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} + 330 x^{4} ({(- 1)}^{7} y^{7}) + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.32

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} + 330 \cdot {(- 1)}^{7} x^{4} y^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.33

Naikkan $- 1$ menjadi pangkat $7$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} + 330 \cdot - 1 x^{4} y^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.34

Kalikan $330$ dengan $- 1$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 {(x)}^{3} {(- y)}^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.35

Terapkan kaidah hasil kali ke $- y$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} ({(- 1)}^{8} y^{8}) + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.36

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 \cdot {(- 1)}^{8} x^{3} y^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.37

Naikkan $- 1$ menjadi pangkat $8$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 \cdot 1 x^{3} y^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.38

Kalikan $165$ dengan $1$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} + 55 {(x)}^{2} {(- y)}^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.39

Terapkan kaidah hasil kali ke $- y$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} + 55 x^{2} ({(- 1)}^{9} y^{9}) + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.40

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} + 55 \cdot {(- 1)}^{9} x^{2} y^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.41

Naikkan $- 1$ menjadi pangkat $9$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} + 55 \cdot - 1 x^{2} y^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.42

Kalikan $55$ dengan $- 1$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} - 55 x^{2} y^{9} + 11 {(x)}^{1} {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.43

Sederhanakan.

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} - 55 x^{2} y^{9} + 11 x {(- y)}^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.44

Terapkan kaidah hasil kali ke $- y$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} - 55 x^{2} y^{9} + 11 x ({(- 1)}^{10} y^{10}) + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.45

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} - 55 x^{2} y^{9} + 11 \cdot {(- 1)}^{10} x y^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.46

Naikkan $- 1$ menjadi pangkat $10$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} - 55 x^{2} y^{9} + 11 \cdot 1 x y^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.47

Kalikan $11$ dengan $1$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} - 55 x^{2} y^{9} + 11 x y^{10} + 1 {(x)}^{0} {(- y)}^{11}$

Langkah 4.48

Kalikan ${(x)}^{0}$ dengan $1$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} - 55 x^{2} y^{9} + 11 x y^{10} + {(x)}^{0} {(- y)}^{11}$

Langkah 4.49

Apa pun yang dinaikkan ke $0$ adalah $1$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} - 55 x^{2} y^{9} + 11 x y^{10} + 1 {(- y)}^{11}$

Langkah 4.50

Kalikan ${(- y)}^{11}$ dengan $1$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} - 55 x^{2} y^{9} + 11 x y^{10} + {(- y)}^{11}$

Langkah 4.51

Terapkan kaidah hasil kali ke $- y$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} - 55 x^{2} y^{9} + 11 x y^{10} + {(- 1)}^{11} y^{11}$

Langkah 4.52

Naikkan $- 1$ menjadi pangkat $11$ .

$x^{11} - 11 x^{10} y + 55 x^{9} y^{2} - 165 x^{8} y^{3} + 330 x^{7} y^{4} - 462 x^{6} y^{5} + 462 x^{5} y^{6} - 330 x^{4} y^{7} + 165 x^{3} y^{8} - 55 x^{2} y^{9} + 11 x y^{10} - y^{11}$