Simplify (2a+3b)^3

${(2 a + 3 b)}^{3}$

Step 1

Use the Binomial Theorem.

${(2 a)}^{3} + 3 {(2 a)}^{2} (3 b) + 3 (2 a) {(3 b)}^{2} + {(3 b)}^{3}$

Step 2

Simplify each term.

Apply the product rule to $2 a$ .

$2^{3} a^{3} + 3 {(2 a)}^{2} (3 b) + 3 (2 a) {(3 b)}^{2} + {(3 b)}^{3}$

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

$8 a^{3} + 3 {(2 a)}^{2} (3 b) + 3 (2 a) {(3 b)}^{2} + {(3 b)}^{3}$

Rewrite using the commutative property of multiplication.

$8 a^{3} + 3 \cdot 3 {(2 a)}^{2} b + 3 (2 a) {(3 b)}^{2} + {(3 b)}^{3}$

Multiply $3$ by $3$ .

$8 a^{3} + 9 {(2 a)}^{2} b + 3 (2 a) {(3 b)}^{2} + {(3 b)}^{3}$

Apply the product rule to $2 a$ .

$8 a^{3} + 9 (2^{2} a^{2}) b + 3 (2 a) {(3 b)}^{2} + {(3 b)}^{3}$

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

$8 a^{3} + 9 (4 a^{2}) b + 3 (2 a) {(3 b)}^{2} + {(3 b)}^{3}$

Multiply $4$ by $9$ .

$8 a^{3} + 36 a^{2} b + 3 (2 a) {(3 b)}^{2} + {(3 b)}^{3}$

Multiply $2$ by $3$ .

$8 a^{3} + 36 a^{2} b + 6 a {(3 b)}^{2} + {(3 b)}^{3}$

Apply the product rule to $3 b$ .

$8 a^{3} + 36 a^{2} b + 6 a (3^{2} b^{2}) + {(3 b)}^{3}$

Rewrite using the commutative property of multiplication.

$8 a^{3} + 36 a^{2} b + 6 \cdot 3^{2} a b^{2} + {(3 b)}^{3}$

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

$8 a^{3} + 36 a^{2} b + 6 \cdot 9 a b^{2} + {(3 b)}^{3}$

Multiply $6$ by $9$ .

$8 a^{3} + 36 a^{2} b + 54 a b^{2} + {(3 b)}^{3}$

Apply the product rule to $3 b$ .

$8 a^{3} + 36 a^{2} b + 54 a b^{2} + 3^{3} b^{3}$

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

$8 a^{3} + 36 a^{2} b + 54 a b^{2} + 27 b^{3}$