Aljabar Contoh

${(3 c + d^{2})}^{6}$

Langkah 1

Gunakan Teorema Binomial.

${(3 c)}^{6} + 6 {(3 c)}^{5} d^{2} + 15 {(3 c)}^{4} {(d^{2})}^{2} + 20 {(3 c)}^{3} {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2

Sederhanakan setiap suku.

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Langkah 2.1

Terapkan kaidah hasil kali ke $3 c$ .

$3^{6} c^{6} + 6 {(3 c)}^{5} d^{2} + 15 {(3 c)}^{4} {(d^{2})}^{2} + 20 {(3 c)}^{3} {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.2

Naikkan $3$ menjadi pangkat $6$ .

$729 c^{6} + 6 {(3 c)}^{5} d^{2} + 15 {(3 c)}^{4} {(d^{2})}^{2} + 20 {(3 c)}^{3} {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.3

Terapkan kaidah hasil kali ke $3 c$ .

$729 c^{6} + 6 (3^{5} c^{5}) d^{2} + 15 {(3 c)}^{4} {(d^{2})}^{2} + 20 {(3 c)}^{3} {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.4

Naikkan $3$ menjadi pangkat $5$ .

$729 c^{6} + 6 (243 c^{5}) d^{2} + 15 {(3 c)}^{4} {(d^{2})}^{2} + 20 {(3 c)}^{3} {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.5

Kalikan $243$ dengan $6$ .

$729 c^{6} + 1458 c^{5} d^{2} + 15 {(3 c)}^{4} {(d^{2})}^{2} + 20 {(3 c)}^{3} {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.6

Terapkan kaidah hasil kali ke $3 c$ .

$729 c^{6} + 1458 c^{5} d^{2} + 15 (3^{4} c^{4}) {(d^{2})}^{2} + 20 {(3 c)}^{3} {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.7

Naikkan $3$ menjadi pangkat $4$ .

$729 c^{6} + 1458 c^{5} d^{2} + 15 (81 c^{4}) {(d^{2})}^{2} + 20 {(3 c)}^{3} {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.8

Kalikan $81$ dengan $15$ .

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} {(d^{2})}^{2} + 20 {(3 c)}^{3} {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.9

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

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Langkah 2.9.1

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

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{2 \cdot 2} + 20 {(3 c)}^{3} {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.9.2

Kalikan $2$ dengan $2$ .

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 20 {(3 c)}^{3} {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.10

Terapkan kaidah hasil kali ke $3 c$ .

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 20 (3^{3} c^{3}) {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.11

Naikkan $3$ menjadi pangkat $3$ .

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 20 (27 c^{3}) {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.12

Kalikan $27$ dengan $20$ .

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 540 c^{3} {(d^{2})}^{3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.13

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

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Langkah 2.13.1

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

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 540 c^{3} d^{2 \cdot 3} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.13.2

Kalikan $2$ dengan $3$ .

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 540 c^{3} d^{6} + 15 {(3 c)}^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.14

Terapkan kaidah hasil kali ke $3 c$ .

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 540 c^{3} d^{6} + 15 (3^{2} c^{2}) {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.15

Naikkan $3$ menjadi pangkat $2$ .

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 540 c^{3} d^{6} + 15 (9 c^{2}) {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.16

Kalikan $9$ dengan $15$ .

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 540 c^{3} d^{6} + 135 c^{2} {(d^{2})}^{4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.17

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

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Langkah 2.17.1

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

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 540 c^{3} d^{6} + 135 c^{2} d^{2 \cdot 4} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.17.2

Kalikan $2$ dengan $4$ .

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 540 c^{3} d^{6} + 135 c^{2} d^{8} + 6 (3 c) {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.18

Kalikan $3$ dengan $6$ .

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 540 c^{3} d^{6} + 135 c^{2} d^{8} + 18 c {(d^{2})}^{5} + {(d^{2})}^{6}$

Langkah 2.19

Kalikan eksponen dalam ${(d^{2})}^{5}$ .

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Langkah 2.19.1

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

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 540 c^{3} d^{6} + 135 c^{2} d^{8} + 18 c d^{2 \cdot 5} + {(d^{2})}^{6}$

Langkah 2.19.2

Kalikan $2$ dengan $5$ .

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 540 c^{3} d^{6} + 135 c^{2} d^{8} + 18 c d^{10} + {(d^{2})}^{6}$

Langkah 2.20

Kalikan eksponen dalam ${(d^{2})}^{6}$ .

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Langkah 2.20.1

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

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 540 c^{3} d^{6} + 135 c^{2} d^{8} + 18 c d^{10} + d^{2 \cdot 6}$

Langkah 2.20.2

Kalikan $2$ dengan $6$ .

$729 c^{6} + 1458 c^{5} d^{2} + 1215 c^{4} d^{4} + 540 c^{3} d^{6} + 135 c^{2} d^{8} + 18 c d^{10} + d^{12}$