Aljabar Contoh

${(- x + 5 y)}^{8}$

Langkah 1

Segitiga Pascal dapat ditampilkan sebagai berikut:

$1$

$1 - 1$

$1 - 2 - 1$

$\dots$

$1 - 6 - 15 - 20 - 15 - 6 - 1$

$1 - 7 - 21 - 35 - 35 - 21 - 7 - 1$

$1 - 8 - 28 - 56 - 70 - 56 - 28 - 8 - 1$

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 ${(- x + 5 y)}^{8}$ $n = 8$ sehingga koefisien dari perluasan akan sesuai dengan garis $9$ .

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 $1 - 8 - 28 - 56 - 70 - 56 - 28 - 8 - 1$ .

$1 a^{8} b^{0} + 8 a^{7} b + 28 a^{6} b^{2} + 56 a^{5} b^{3} + 70 a^{4} b^{4} + 56 a^{3} b^{5} + 28 a^{2} b^{6} + 8 a b^{7} + 1 a^{0} b^{8}$

Langkah 3

Substitusikan nilai-nilai aktual dari $a$ $- x$ dan $b$ $5 y$ ke dalam pernyataannya.

$1 {(- x)}^{8} {(5 y)}^{0} + 8 {(- x)}^{7} {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 4.1

Kalikan ${(- x)}^{8}$ dengan $1$ .

${(- x)}^{8} {(5 y)}^{0} + 8 {(- x)}^{7} {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.2

Terapkan kaidah hasil kali ke $- x$ .

${(- 1)}^{8} x^{8} {(5 y)}^{0} + 8 {(- x)}^{7} {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.3

Naikkan $- 1$ menjadi pangkat $8$ .

$1 x^{8} {(5 y)}^{0} + 8 {(- x)}^{7} {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.4

Kalikan $x^{8}$ dengan $1$ .

$x^{8} {(5 y)}^{0} + 8 {(- x)}^{7} {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.5

Terapkan kaidah hasil kali ke $5 y$ .

$x^{8} (5^{0} y^{0}) + 8 {(- x)}^{7} {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.6

Tulis kembali menggunakan sifat komutatif dari perkalian.

$5^{0} x^{8} y^{0} + 8 {(- x)}^{7} {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.7

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

$1 x^{8} y^{0} + 8 {(- x)}^{7} {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.8

Kalikan $x^{8}$ dengan $1$ .

$x^{8} y^{0} + 8 {(- x)}^{7} {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.9

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

$x^{8} \cdot 1 + 8 {(- x)}^{7} {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.10

Kalikan $x^{8}$ dengan $1$ .

$x^{8} + 8 {(- x)}^{7} {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.11

Terapkan kaidah hasil kali ke $- x$ .

$x^{8} + 8 ({(- 1)}^{7} x^{7}) {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.12

Naikkan $- 1$ menjadi pangkat $7$ .

$x^{8} + 8 (- x^{7}) {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.13

Kalikan $- 1$ dengan $8$ .

$x^{8} - 8 x^{7} {(5 y)}^{1} + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.14

Sederhanakan.

$x^{8} - 8 x^{7} (5 y) + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.15

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{8} - 8 \cdot 5 x^{7} y + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.16

Kalikan $- 8$ dengan $5$ .

$x^{8} - 40 x^{7} y + 28 {(- x)}^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.17

Terapkan kaidah hasil kali ke $- x$ .

$x^{8} - 40 x^{7} y + 28 ({(- 1)}^{6} x^{6}) {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.18

Naikkan $- 1$ menjadi pangkat $6$ .

$x^{8} - 40 x^{7} y + 28 (1 x^{6}) {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.19

Kalikan $x^{6}$ dengan $1$ .

$x^{8} - 40 x^{7} y + 28 x^{6} {(5 y)}^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.20

Terapkan kaidah hasil kali ke $5 y$ .

$x^{8} - 40 x^{7} y + 28 x^{6} (5^{2} y^{2}) + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.21

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{8} - 40 x^{7} y + 28 \cdot 5^{2} x^{6} y^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.22

Naikkan $5$ menjadi pangkat $2$ .

$x^{8} - 40 x^{7} y + 28 \cdot 25 x^{6} y^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.23

Kalikan $28$ dengan $25$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} + 56 {(- x)}^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.24

Terapkan kaidah hasil kali ke $- x$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} + 56 ({(- 1)}^{5} x^{5}) {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.25

Naikkan $- 1$ menjadi pangkat $5$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} + 56 (- x^{5}) {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.26

Kalikan $- 1$ dengan $56$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 56 x^{5} {(5 y)}^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.27

Terapkan kaidah hasil kali ke $5 y$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 56 x^{5} (5^{3} y^{3}) + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.28

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 56 \cdot 5^{3} x^{5} y^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.29

Naikkan $5$ menjadi pangkat $3$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 56 \cdot 125 x^{5} y^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.30

Kalikan $- 56$ dengan $125$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 70 {(- x)}^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.31

Terapkan kaidah hasil kali ke $- x$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 70 ({(- 1)}^{4} x^{4}) {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.32

Naikkan $- 1$ menjadi pangkat $4$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 70 (1 x^{4}) {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.33

Kalikan $x^{4}$ dengan $1$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 70 x^{4} {(5 y)}^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.34

Terapkan kaidah hasil kali ke $5 y$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 70 x^{4} (5^{4} y^{4}) + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.35

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 70 \cdot 5^{4} x^{4} y^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.36

Naikkan $5$ menjadi pangkat $4$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 70 \cdot 625 x^{4} y^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.37

Kalikan $70$ dengan $625$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} + 56 {(- x)}^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.38

Terapkan kaidah hasil kali ke $- x$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} + 56 ({(- 1)}^{3} x^{3}) {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.39

Naikkan $- 1$ menjadi pangkat $3$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} + 56 (- x^{3}) {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.40

Kalikan $- 1$ dengan $56$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 56 x^{3} {(5 y)}^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.41

Terapkan kaidah hasil kali ke $5 y$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 56 x^{3} (5^{5} y^{5}) + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.42

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 56 \cdot 5^{5} x^{3} y^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.43

Naikkan $5$ menjadi pangkat $5$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 56 \cdot 3125 x^{3} y^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.44

Kalikan $- 56$ dengan $3125$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 28 {(- x)}^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.45

Terapkan kaidah hasil kali ke $- x$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 28 ({(- 1)}^{2} x^{2}) {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.46

Naikkan $- 1$ menjadi pangkat $2$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 28 (1 x^{2}) {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.47

Kalikan $x^{2}$ dengan $1$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 28 x^{2} {(5 y)}^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.48

Terapkan kaidah hasil kali ke $5 y$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 28 x^{2} (5^{6} y^{6}) + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.49

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 28 \cdot 5^{6} x^{2} y^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.50

Naikkan $5$ menjadi pangkat $6$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 28 \cdot 15625 x^{2} y^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.51

Kalikan $28$ dengan $15625$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} + 8 {(- x)}^{1} {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.52

Sederhanakan.

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} + 8 (- x) {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.53

Kalikan $- 1$ dengan $8$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} - 8 x {(5 y)}^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.54

Terapkan kaidah hasil kali ke $5 y$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} - 8 x (5^{7} y^{7}) + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.55

Tulis kembali menggunakan sifat komutatif dari perkalian.

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} - 8 \cdot 5^{7} x y^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.56

Naikkan $5$ menjadi pangkat $7$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} - 8 \cdot 78125 x y^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.57

Kalikan $- 8$ dengan $78125$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} - 625000 x y^{7} + 1 {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.58

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

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} - 625000 x y^{7} + {(- x)}^{0} {(5 y)}^{8}$

Langkah 4.59

Terapkan kaidah hasil kali ke $- x$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} - 625000 x y^{7} + {(- 1)}^{0} x^{0} {(5 y)}^{8}$

Langkah 4.60

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

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} - 625000 x y^{7} + 1 x^{0} {(5 y)}^{8}$

Langkah 4.61

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

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} - 625000 x y^{7} + x^{0} {(5 y)}^{8}$

Langkah 4.62

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

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} - 625000 x y^{7} + 1 {(5 y)}^{8}$

Langkah 4.63

Kalikan ${(5 y)}^{8}$ dengan $1$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} - 625000 x y^{7} + {(5 y)}^{8}$

Langkah 4.64

Terapkan kaidah hasil kali ke $5 y$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} - 625000 x y^{7} + 5^{8} y^{8}$

Langkah 4.65

Naikkan $5$ menjadi pangkat $8$ .

$x^{8} - 40 x^{7} y + 700 x^{6} y^{2} - 7000 x^{5} y^{3} + 43750 x^{4} y^{4} - 175000 x^{3} y^{5} + 437500 x^{2} y^{6} - 625000 x y^{7} + 390625 y^{8}$