Aljabar Contoh

${(2 x^{2} + y^{2})}^{4}$

Langkah 1

Gunakan teorema pengembangan binomial untuk menentukan setiap suku. Teorema binomial menyatakan ${(a + b)}^{n} = \sum_{k = 0}^{n} n C k \cdot (a^{n - k} b^{k})$ .

$\sum_{k = 0}^{4} \frac{4!}{(4 - k)! k!} \cdot {(2 x^{2})}^{4 - k} \cdot {(y^{2})}^{k}$

Langkah 2

Perluas penjumlahannya.

$\frac{4!}{(4 - 0)! 0!} \cdot {(2 x^{2})}^{4 - 0} \cdot {(y^{2})}^{0} + \frac{4!}{(4 - 1)! 1!} \cdot {(2 x^{2})}^{4 - 1} \cdot {(y^{2})}^{1} + \frac{4!}{(4 - 2)! 2!} \cdot {(2 x^{2})}^{4 - 2} \cdot {(y^{2})}^{2} + \frac{4!}{(4 - 3)! 3!} \cdot {(2 x^{2})}^{4 - 3} \cdot {(y^{2})}^{3} + \frac{4!}{(4 - 4)! 4!} \cdot {(2 x^{2})}^{4 - 4} \cdot {(y^{2})}^{4}$

Langkah 3

Sederhanakan eksponen untuk setiap suku dari pengembangan.

$1 \cdot {(2 x^{2})}^{4} \cdot {(y^{2})}^{0} + 4 \cdot {(2 x^{2})}^{3} \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 4.1

Kalikan ${(2 x^{2})}^{4}$ dengan $1$ .

${(2 x^{2})}^{4} \cdot {(y^{2})}^{0} + 4 \cdot {(2 x^{2})}^{3} \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.2

Terapkan kaidah hasil kali ke $2 x^{2}$ .

$2^{4} {(x^{2})}^{4} \cdot {(y^{2})}^{0} + 4 \cdot {(2 x^{2})}^{3} \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.3

Naikkan $2$ menjadi pangkat $4$ .

$16 {(x^{2})}^{4} \cdot {(y^{2})}^{0} + 4 \cdot {(2 x^{2})}^{3} \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.4

Kalikan eksponen dalam ${(x^{2})}^{4}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.4.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$16 x^{2 \cdot 4} \cdot {(y^{2})}^{0} + 4 \cdot {(2 x^{2})}^{3} \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.4.2

Kalikan $2$ dengan $4$ .

$16 x^{8} \cdot {(y^{2})}^{0} + 4 \cdot {(2 x^{2})}^{3} \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.5

Kalikan eksponen dalam ${(y^{2})}^{0}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.5.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$16 x^{8} \cdot y^{2 \cdot 0} + 4 \cdot {(2 x^{2})}^{3} \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.5.2

Kalikan $2$ dengan $0$ .

$16 x^{8} \cdot y^{0} + 4 \cdot {(2 x^{2})}^{3} \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.6

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

$16 x^{8} \cdot 1 + 4 \cdot {(2 x^{2})}^{3} \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.7

Kalikan $16$ dengan $1$ .

$16 x^{8} + 4 \cdot {(2 x^{2})}^{3} \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.8

Terapkan kaidah hasil kali ke $2 x^{2}$ .

$16 x^{8} + 4 \cdot (2^{3} {(x^{2})}^{3}) \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.9

Naikkan $2$ menjadi pangkat $3$ .

$16 x^{8} + 4 \cdot (8 {(x^{2})}^{3}) \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.10

Kalikan eksponen dalam ${(x^{2})}^{3}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.10.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$16 x^{8} + 4 \cdot (8 x^{2 \cdot 3}) \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.10.2

Kalikan $2$ dengan $3$ .

$16 x^{8} + 4 \cdot (8 x^{6}) \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.11

Kalikan $8$ dengan $4$ .

$16 x^{8} + 32 x^{6} \cdot {(y^{2})}^{1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.12

Kalikan eksponen dalam ${(y^{2})}^{1}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.12.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$16 x^{8} + 32 x^{6} \cdot y^{2 \cdot 1} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.12.2

Kalikan $2$ dengan $1$ .

$16 x^{8} + 32 x^{6} \cdot y^{2} + 6 \cdot {(2 x^{2})}^{2} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.13

Terapkan kaidah hasil kali ke $2 x^{2}$ .

$16 x^{8} + 32 x^{6} y^{2} + 6 \cdot (2^{2} {(x^{2})}^{2}) \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.14

Naikkan $2$ menjadi pangkat $2$ .

$16 x^{8} + 32 x^{6} y^{2} + 6 \cdot (4 {(x^{2})}^{2}) \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.15

Kalikan eksponen dalam ${(x^{2})}^{2}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.15.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$16 x^{8} + 32 x^{6} y^{2} + 6 \cdot (4 x^{2 \cdot 2}) \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.15.2

Kalikan $2$ dengan $2$ .

$16 x^{8} + 32 x^{6} y^{2} + 6 \cdot (4 x^{4}) \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.16

Kalikan $4$ dengan $6$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} \cdot {(y^{2})}^{2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.17

Kalikan eksponen dalam ${(y^{2})}^{2}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.17.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} \cdot y^{2 \cdot 2} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.17.2

Kalikan $2$ dengan $2$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} \cdot y^{4} + 4 \cdot {(2 x^{2})}^{1} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.18

Sederhanakan.

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 4 \cdot (2 x^{2}) \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.19

Kalikan $2$ dengan $4$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 8 x^{2} \cdot {(y^{2})}^{3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.20

Kalikan eksponen dalam ${(y^{2})}^{3}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.20.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 8 x^{2} \cdot y^{2 \cdot 3} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.20.2

Kalikan $2$ dengan $3$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 8 x^{2} \cdot y^{6} + 1 \cdot {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.21

Kalikan ${(2 x^{2})}^{0}$ dengan $1$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 8 x^{2} y^{6} + {(2 x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.22

Terapkan kaidah hasil kali ke $2 x^{2}$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 8 x^{2} y^{6} + 2^{0} {(x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.23

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

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 8 x^{2} y^{6} + 1 {(x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.24

Kalikan ${(x^{2})}^{0}$ dengan $1$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 8 x^{2} y^{6} + {(x^{2})}^{0} \cdot {(y^{2})}^{4}$

Langkah 4.25

Kalikan eksponen dalam ${(x^{2})}^{0}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.25.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 8 x^{2} y^{6} + x^{2 \cdot 0} \cdot {(y^{2})}^{4}$

Langkah 4.25.2

Kalikan $2$ dengan $0$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 8 x^{2} y^{6} + x^{0} \cdot {(y^{2})}^{4}$

Langkah 4.26

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

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 8 x^{2} y^{6} + 1 \cdot {(y^{2})}^{4}$

Langkah 4.27

Kalikan ${(y^{2})}^{4}$ dengan $1$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 8 x^{2} y^{6} + {(y^{2})}^{4}$

Langkah 4.28

Kalikan eksponen dalam ${(y^{2})}^{4}$ .

Ketuk untuk lebih banyak langkah...

Langkah 4.28.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 8 x^{2} y^{6} + y^{2 \cdot 4}$

Langkah 4.28.2

Kalikan $2$ dengan $4$ .

$16 x^{8} + 32 x^{6} y^{2} + 24 x^{4} y^{4} + 8 x^{2} y^{6} + y^{8}$