Simplify (x+3)^3

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Multiply $3$ by $3$ .

$x^{3} + 9 x^{2} + 3 x \cdot 3^{2} + 3^{3}$

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

Move $3^{2}$ .

$x^{3} + 9 x^{2} + 3^{2} \cdot 3 x + 3^{3}$

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

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

$x^{3} + 9 x^{2} + 3^{2} \cdot 3^{1} x + 3^{3}$

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

$x^{3} + 9 x^{2} + 3^{2 + 1} x + 3^{3}$

Add $2$ and $1$ .

$x^{3} + 9 x^{2} + 3^{3} x + 3^{3}$

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

$x^{3} + 9 x^{2} + 27 x + 3^{3}$

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

$x^{3} + 9 x^{2} + 27 x + 27$