Simplify (2x+3)^3

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Apply the product rule to $2 x$ .

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

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

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

Apply the product rule to $2 x$ .

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

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

$8 x^{3} + 3 (4 x^{2}) \cdot 3 + 3 (2 x) \cdot 3^{2} + 3^{3}$

Multiply $4$ by $3$ .

$8 x^{3} + 12 x^{2} \cdot 3 + 3 (2 x) \cdot 3^{2} + 3^{3}$

Multiply $3$ by $12$ .

$8 x^{3} + 36 x^{2} + 3 (2 x) \cdot 3^{2} + 3^{3}$

Multiply $3$ by $3^{2}$ by adding the exponents.

Move $3^{2}$ .

$8 x^{3} + 36 x^{2} + 3^{2} \cdot 3 (2 x) + 3^{3}$

Multiply $3^{2}$ by $3$ .

Raise $3$ to the power of $1$ .

$8 x^{3} + 36 x^{2} + 3^{2} \cdot 3^{1} (2 x) + 3^{3}$

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

$8 x^{3} + 36 x^{2} + 3^{2 + 1} (2 x) + 3^{3}$

Add $2$ and $1$ .

$8 x^{3} + 36 x^{2} + 3^{3} (2 x) + 3^{3}$

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

$8 x^{3} + 36 x^{2} + 27 (2 x) + 3^{3}$

Multiply $2$ by $27$ .

$8 x^{3} + 36 x^{2} + 54 x + 3^{3}$

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

$8 x^{3} + 36 x^{2} + 54 x + 27$