Algebra Examples

${(6 x + 2 y)}^{3}$

Step 1

Use the Binomial Theorem.

${(6 x)}^{3} + 3 {(6 x)}^{2} (2 y) + 3 (6 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $6 x$ .

$6^{3} x^{3} + 3 {(6 x)}^{2} (2 y) + 3 (6 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.2

Raise $6$ to the power of $3$ .

$216 x^{3} + 3 {(6 x)}^{2} (2 y) + 3 (6 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.3

Rewrite using the commutative property of multiplication.

$216 x^{3} + 3 \cdot 2 {(6 x)}^{2} y + 3 (6 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.4

Multiply $3$ by $2$ .

$216 x^{3} + 6 {(6 x)}^{2} y + 3 (6 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.5

Apply the product rule to $6 x$ .

$216 x^{3} + 6 (6^{2} x^{2}) y + 3 (6 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.6

Multiply $6$ by $6^{2}$ by adding the exponents.

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Step 2.6.1

Move $6^{2}$ .

$216 x^{3} + 6^{2} \cdot 6 x^{2} y + 3 (6 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.6.2

Multiply $6^{2}$ by $6$ .

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Step 2.6.2.1

Raise $6$ to the power of $1$ .

$216 x^{3} + 6^{2} \cdot 6^{1} x^{2} y + 3 (6 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.6.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$216 x^{3} + 6^{2 + 1} x^{2} y + 3 (6 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.6.3

Add $2$ and $1$ .

$216 x^{3} + 6^{3} x^{2} y + 3 (6 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.7

Raise $6$ to the power of $3$ .

$216 x^{3} + 216 x^{2} y + 3 (6 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.8

Multiply $6$ by $3$ .

$216 x^{3} + 216 x^{2} y + 18 x {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.9

Apply the product rule to $2 y$ .

$216 x^{3} + 216 x^{2} y + 18 x (2^{2} y^{2}) + {(2 y)}^{3}$

Step 2.10

Rewrite using the commutative property of multiplication.

$216 x^{3} + 216 x^{2} y + 18 \cdot 2^{2} x y^{2} + {(2 y)}^{3}$

Step 2.11

Raise $2$ to the power of $2$ .

$216 x^{3} + 216 x^{2} y + 18 \cdot 4 x y^{2} + {(2 y)}^{3}$

Step 2.12

Multiply $18$ by $4$ .

$216 x^{3} + 216 x^{2} y + 72 x y^{2} + {(2 y)}^{3}$

Step 2.13

Apply the product rule to $2 y$ .

$216 x^{3} + 216 x^{2} y + 72 x y^{2} + 2^{3} y^{3}$

Step 2.14

Raise $2$ to the power of $3$ .

$216 x^{3} + 216 x^{2} y + 72 x y^{2} + 8 y^{3}$