Aljabar Contoh

${(\sqrt{2} x + \frac{1}{2} y)}^{4}$

Langkah 1

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

$\sum_{k = 0}^{4} \frac{4!}{(4 - k)! k!} \cdot {(\sqrt{2} x)}^{4 - k} \cdot {(\frac{1}{2} y)}^{k}$

Langkah 2

Perluas penjumlahannya.

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

Langkah 3

Sederhanakan eksponen untuk setiap suku dari pengembangan.

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

Langkah 4

Sederhanakan setiap suku.

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Langkah 4.1

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

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

Langkah 4.2

Terapkan kaidah hasil kali ke $\sqrt{2} x$ .

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

Langkah 4.3

Tulis kembali ${\sqrt{2}}^{4}$ sebagai $2^{2}$ .

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Langkah 4.3.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{2}$ sebagai $2^{\frac{1}{2}}$ .

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

Langkah 4.3.2

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

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

Langkah 4.3.3

Gabungkan $\frac{1}{2}$ dan $4$ .

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

Langkah 4.3.4

Hapus faktor persekutuan dari $4$ dan $2$ .

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Langkah 4.3.4.1

Faktorkan $2$ dari $4$ .

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

Langkah 4.3.4.2

Batalkan faktor persekutuan.

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Langkah 4.3.4.2.1

Faktorkan $2$ dari $2$ .

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

Langkah 4.3.4.2.2

Batalkan faktor persekutuan.

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

Langkah 4.3.4.2.3

Tulis kembali pernyataannya.

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

Langkah 4.3.4.2.4

Bagilah $2$ dengan $1$ .

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

Langkah 4.4

Naikkan $2$ menjadi pangkat $2$ .

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

Langkah 4.5

Gabungkan $\frac{1}{2}$ dan $y$ .

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

Langkah 4.6

Terapkan kaidah hasil kali ke $\frac{y}{2}$ .

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

Langkah 4.7

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

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

Langkah 4.8

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

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

Langkah 4.9

Bagilah $1$ dengan $1$ .

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

Langkah 4.10

Kalikan $4$ dengan $1$ .

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

Langkah 4.11

Terapkan kaidah hasil kali ke $\sqrt{2} x$ .

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

Langkah 4.12

Tulis kembali ${\sqrt{2}}^{3}$ sebagai $\sqrt{2^{3}}$ .

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

Langkah 4.13

Naikkan $2$ menjadi pangkat $3$ .

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

Langkah 4.14

Tulis kembali $8$ sebagai $2^{2} \cdot 2$ .

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Langkah 4.14.1

Faktorkan $4$ dari $8$ .

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

Langkah 4.14.2

Tulis kembali $4$ sebagai $2^{2}$ .

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

Langkah 4.15

Mengeluarkan suku-suku dari bawah akar.

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

Langkah 4.16

Kalikan $2$ dengan $4$ .

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

Langkah 4.17

Gabungkan $\frac{1}{2}$ dan $y$ .

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

Langkah 4.18

Sederhanakan.

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

Langkah 4.19

Batalkan faktor persekutuan dari $2$ .

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Langkah 4.19.1

Faktorkan $2$ dari $8 \sqrt{2} x^{3}$ .

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

Langkah 4.19.2

Batalkan faktor persekutuan.

Langkah 4.19.3

Tulis kembali pernyataannya.

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

Langkah 4.20

Terapkan kaidah hasil kali ke $\sqrt{2} x$ .

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

Langkah 4.21

Tulis kembali ${\sqrt{2}}^{2}$ sebagai $2$ .

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Langkah 4.21.1

Gunakan $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ untuk menuliskan kembali $\sqrt{2}$ sebagai $2^{\frac{1}{2}}$ .

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

Langkah 4.21.2

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

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

Langkah 4.21.3

Gabungkan $\frac{1}{2}$ dan $2$ .

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

Langkah 4.21.4

Batalkan faktor persekutuan dari $2$ .

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Langkah 4.21.4.1

Batalkan faktor persekutuan.

Langkah 4.21.4.2

Tulis kembali pernyataannya.

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

Langkah 4.21.5

Evaluasi eksponennya.

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

Langkah 4.22

Kalikan $2$ dengan $6$ .

$4 x^{4} + 4 \sqrt{2} x^{3} y + 12 x^{2} \cdot {(\frac{1}{2} y)}^{2} + 4 \cdot {(\sqrt{2} x)}^{1} \cdot {(\frac{1}{2} y)}^{3} + 1 \cdot {(\sqrt{2} x)}^{0} \cdot {(\frac{1}{2} y)}^{4}$

Langkah 4.23

Gabungkan $\frac{1}{2}$ dan $y$ .

$4 x^{4} + 4 \sqrt{2} x^{3} y + 12 x^{2} \cdot {(\frac{y}{2})}^{2} + 4 \cdot {(\sqrt{2} x)}^{1} \cdot {(\frac{1}{2} y)}^{3} + 1 \cdot {(\sqrt{2} x)}^{0} \cdot {(\frac{1}{2} y)}^{4}$

Langkah 4.24

Terapkan kaidah hasil kali ke $\frac{y}{2}$ .

$4 x^{4} + 4 \sqrt{2} x^{3} y + 12 x^{2} \cdot \frac{y^{2}}{2^{2}} + 4 \cdot {(\sqrt{2} x)}^{1} \cdot {(\frac{1}{2} y)}^{3} + 1 \cdot {(\sqrt{2} x)}^{0} \cdot {(\frac{1}{2} y)}^{4}$

Langkah 4.25

Naikkan $2$ menjadi pangkat $2$ .

$4 x^{4} + 4 \sqrt{2} x^{3} y + 12 x^{2} \cdot \frac{y^{2}}{4} + 4 \cdot {(\sqrt{2} x)}^{1} \cdot {(\frac{1}{2} y)}^{3} + 1 \cdot {(\sqrt{2} x)}^{0} \cdot {(\frac{1}{2} y)}^{4}$

Langkah 4.26

Batalkan faktor persekutuan dari $4$ .

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Langkah 4.26.1

Faktorkan $4$ dari $12 x^{2}$ .

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

Langkah 4.26.2

Batalkan faktor persekutuan.

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

Langkah 4.26.3

Tulis kembali pernyataannya.

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

Langkah 4.27

Sederhanakan.

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

Langkah 4.28

Gabungkan $\frac{1}{2}$ dan $y$ .

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

Langkah 4.29

Terapkan kaidah hasil kali ke $\frac{y}{2}$ .

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

Langkah 4.30

Naikkan $2$ menjadi pangkat $3$ .

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

Langkah 4.31

Batalkan faktor persekutuan dari $4$ .

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Langkah 4.31.1

Faktorkan $4$ dari $4 \sqrt{2} x$ .

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

Langkah 4.31.2

Faktorkan $4$ dari $8$ .

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

Langkah 4.31.3

Batalkan faktor persekutuan.

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

Langkah 4.31.4

Tulis kembali pernyataannya.

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

Langkah 4.32

Gabungkan $\sqrt{2}$ dan $\frac{y^{3}}{2}$ .

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

Langkah 4.33

Gabungkan $x$ dan $\frac{\sqrt{2} y^{3}}{2}$ .

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

Langkah 4.34

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

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

Langkah 4.35

Terapkan kaidah hasil kali ke $\sqrt{2} x$ .

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

Langkah 4.36

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

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

Langkah 4.37

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

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

Langkah 4.38

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

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

Langkah 4.39

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

$4 x^{4} + 4 \sqrt{2} x^{3} y + 3 x^{2} y^{2} + \frac{x \sqrt{2} y^{3}}{2} + {(\frac{1}{2} y)}^{4}$

Langkah 4.40

Gabungkan $\frac{1}{2}$ dan $y$ .

$4 x^{4} + 4 \sqrt{2} x^{3} y + 3 x^{2} y^{2} + \frac{x \sqrt{2} y^{3}}{2} + {(\frac{y}{2})}^{4}$

Langkah 4.41

Terapkan kaidah hasil kali ke $\frac{y}{2}$ .

$4 x^{4} + 4 \sqrt{2} x^{3} y + 3 x^{2} y^{2} + \frac{x \sqrt{2} y^{3}}{2} + \frac{y^{4}}{2^{4}}$

Langkah 4.42

Naikkan $2$ menjadi pangkat $4$ .

$4 x^{4} + 4 \sqrt{2} x^{3} y + 3 x^{2} y^{2} + \frac{x \sqrt{2} y^{3}}{2} + \frac{y^{4}}{16}$