Prakalkulus Contoh

5 {(x^{6} + 1)}^{4} (6 x^{5}) {(3 x + 2)}^{3} + 3 {(3 x + 2)}^{2} (3) {(x^{6} + 1)}^{5}

$5 {(x^{6} + 1)}^{4} (6 x^{5}) {(3 x + 2)}^{3} + 3 {(3 x + 2)}^{2} (3) {(x^{6} + 1)}^{5}$

Langkah 1

Kalikan

3 {(3 x + 2)}^{2}

$3 {(3 x + 2)}^{2}$ dengan

3

$3$ .

5 {(x^{6} + 1)}^{4} (6 x^{5}) {(3 x + 2)}^{3} + 3 {(3 x + 2)}^{2} \cdot 3 {(x^{6} + 1)}^{5}

$5 {(x^{6} + 1)}^{4} (6 x^{5}) {(3 x + 2)}^{3} + 3 {(3 x + 2)}^{2} \cdot 3 {(x^{6} + 1)}^{5}$

Langkah 2

Faktorkan

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

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

5 {(x^{6} + 1)}^{4} (6 x^{5}) {(3 x + 2)}^{3} + 3 {(3 x + 2)}^{2} \cdot 3 {(x^{6} + 1)}^{5}

$5 {(x^{6} + 1)}^{4} (6 x^{5}) {(3 x + 2)}^{3} + 3 {(3 x + 2)}^{2} \cdot 3 {(x^{6} + 1)}^{5}$ .

Ketuk untuk lebih banyak langkah...

Langkah 2.1

Faktorkan

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

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

5 {(x^{6} + 1)}^{4} (6 x^{5}) {(3 x + 2)}^{3}

$5 {(x^{6} + 1)}^{4} (6 x^{5}) {(3 x + 2)}^{3}$ .

{(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2)) + 3 {(3 x + 2)}^{2} \cdot 3 {(x^{6} + 1)}^{5}

${(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2)) + 3 {(3 x + 2)}^{2} \cdot 3 {(x^{6} + 1)}^{5}$

Langkah 2.2

Faktorkan

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

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

3 {(3 x + 2)}^{2} \cdot 3 {(x^{6} + 1)}^{5}

$3 {(3 x + 2)}^{2} \cdot 3 {(x^{6} + 1)}^{5}$ .

{(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2)) + {(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (3 (x^{6} + 1))

${(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2)) + {(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (3 (x^{6} + 1))$

Langkah 2.3

Faktorkan

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

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

{(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2)) + {(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (3 (x^{6} + 1))

${(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2)) + {(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (3 (x^{6} + 1))$ .

{(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))

${(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))$

{(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))

${(x^{6} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))$

Langkah 3

Tulis kembali

x^{6}

$x^{6}$ sebagai

{(x^{2})}^{3}

${(x^{2})}^{3}$ .

{({(x^{2})}^{3} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))

${({(x^{2})}^{3} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))$

Langkah 4

Tulis kembali

1

$1$ sebagai

1^{3}

$1^{3}$ .

{({(x^{2})}^{3} + 1^{3})}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))

${({(x^{2})}^{3} + 1^{3})}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))$

Langkah 5

Karena kedua suku adalah pangkat tiga sempurna, faktorkan menggunakan rumus penjumlahan pangkat tiga.

a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ di mana

a = x^{2}

$a = x^{2}$ dan

b = 1

$b = 1$ .

{((x^{2} + 1) ({(x^{2})}^{2} - x^{2} \cdot 1 + 1^{2}))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))

${((x^{2} + 1) ({(x^{2})}^{2} - x^{2} \cdot 1 + 1^{2}))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))$

Langkah 6

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 6.1

Kalikan eksponen dalam

{(x^{2})}^{2}

${(x^{2})}^{2}$ .

Ketuk untuk lebih banyak langkah...

Langkah 6.1.1

Terapkan kaidah pangkat dan perkalian eksponen,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

{((x^{2} + 1) (x^{2 \cdot 2} - x^{2} \cdot 1 + 1^{2}))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))

${((x^{2} + 1) (x^{2 \cdot 2} - x^{2} \cdot 1 + 1^{2}))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))$

Langkah 6.1.2

Kalikan

2

$2$ dengan

2

$2$ .

{((x^{2} + 1) (x^{4} - x^{2} \cdot 1 + 1^{2}))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))

${((x^{2} + 1) (x^{4} - x^{2} \cdot 1 + 1^{2}))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))$

{((x^{2} + 1) (x^{4} - x^{2} \cdot 1 + 1^{2}))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))

${((x^{2} + 1) (x^{4} - x^{2} \cdot 1 + 1^{2}))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))$

Langkah 6.2

Kalikan

- 1

$- 1$ dengan

1

$1$ .

{((x^{2} + 1) (x^{4} - x^{2} + 1^{2}))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))

${((x^{2} + 1) (x^{4} - x^{2} + 1^{2}))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))$

Langkah 6.3

Satu dipangkat berapa pun sama dengan satu.

{((x^{2} + 1) (x^{4} - x^{2} + 1))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))

${((x^{2} + 1) (x^{4} - x^{2} + 1))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))$

{((x^{2} + 1) (x^{4} - x^{2} + 1))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))

${((x^{2} + 1) (x^{4} - x^{2} + 1))}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))$

Langkah 7

Terapkan kaidah hasil kali ke

(x^{2} + 1) (x^{4} - x^{2} + 1)

$(x^{2} + 1) (x^{4} - x^{2} + 1)$ .

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (5 (2 x^{5}) (3 x + 2) + 3 (x^{6} + 1))$

Langkah 8

Kalikan

2

$2$ dengan

5

$5$ .

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 x^{5} (3 x + 2) + 3 (x^{6} + 1))

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 x^{5} (3 x + 2) + 3 (x^{6} + 1))$

Langkah 9

Terapkan sifat distributif.

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 x^{5} (3 x) + 10 x^{5} \cdot 2 + 3 (x^{6} + 1))

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 x^{5} (3 x) + 10 x^{5} \cdot 2 + 3 (x^{6} + 1))$

Langkah 10

Tulis kembali menggunakan sifat komutatif dari perkalian.

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 x^{5} x + 10 x^{5} \cdot 2 + 3 (x^{6} + 1))

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 x^{5} x + 10 x^{5} \cdot 2 + 3 (x^{6} + 1))$

Langkah 11

Kalikan

2

$2$ dengan

10

$10$ .

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 x^{5} x + 20 x^{5} + 3 (x^{6} + 1))

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 x^{5} x + 20 x^{5} + 3 (x^{6} + 1))$

Langkah 12

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 12.1

Kalikan

x^{5}

$x^{5}$ dengan

x

$x$ dengan menambahkan eksponennya.

Ketuk untuk lebih banyak langkah...

Langkah 12.1.1

Pindahkan

x

$x$ .

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 (x \cdot x^{5}) + 20 x^{5} + 3 (x^{6} + 1))

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 (x \cdot x^{5}) + 20 x^{5} + 3 (x^{6} + 1))$

Langkah 12.1.2

Kalikan

x

$x$ dengan

x^{5}

$x^{5}$ .

Ketuk untuk lebih banyak langkah...

Langkah 12.1.2.1

Naikkan

x

$x$ menjadi pangkat

1

$1$ .

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 (x^{1} x^{5}) + 20 x^{5} + 3 (x^{6} + 1))

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 (x^{1} x^{5}) + 20 x^{5} + 3 (x^{6} + 1))$

Langkah 12.1.2.2

Gunakan kaidah pangkat

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 x^{1 + 5} + 20 x^{5} + 3 (x^{6} + 1))

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 x^{1 + 5} + 20 x^{5} + 3 (x^{6} + 1))$

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 x^{1 + 5} + 20 x^{5} + 3 (x^{6} + 1))

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 x^{1 + 5} + 20 x^{5} + 3 (x^{6} + 1))$

Langkah 12.1.3

Tambahkan

1

$1$ dan

5

$5$ .

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 x^{6} + 20 x^{5} + 3 (x^{6} + 1))

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 x^{6} + 20 x^{5} + 3 (x^{6} + 1))$

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 x^{6} + 20 x^{5} + 3 (x^{6} + 1))

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (10 \cdot 3 x^{6} + 20 x^{5} + 3 (x^{6} + 1))$

Langkah 12.2

Kalikan

10

$10$ dengan

3

$3$ .

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (30 x^{6} + 20 x^{5} + 3 (x^{6} + 1))

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (30 x^{6} + 20 x^{5} + 3 (x^{6} + 1))$

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (30 x^{6} + 20 x^{5} + 3 (x^{6} + 1))

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (30 x^{6} + 20 x^{5} + 3 (x^{6} + 1))$

Langkah 13

Terapkan sifat distributif.

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (30 x^{6} + 20 x^{5} + 3 x^{6} + 3 \cdot 1)

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (30 x^{6} + 20 x^{5} + 3 x^{6} + 3 \cdot 1)$

Langkah 14

Kalikan

3

$3$ dengan

1

$1$ .

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (30 x^{6} + 20 x^{5} + 3 x^{6} + 3)

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (30 x^{6} + 20 x^{5} + 3 x^{6} + 3)$

Langkah 15

Tambahkan

30 x^{6}

$30 x^{6}$ dan

3 x^{6}

$3 x^{6}$ .

{(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (33 x^{6} + 20 x^{5} + 3)

${(x^{2} + 1)}^{4} {(x^{4} - x^{2} + 1)}^{4} \cdot 3 {(3 x + 2)}^{2} (33 x^{6} + 20 x^{5} + 3)$