Simplify (x+3)^4

${(x + 3)}^{4}$

Step 1

Use the Binomial Theorem.

$x^{4} + 4 x^{3} \cdot 3 + 6 x^{2} \cdot 3^{2} + 4 x \cdot 3^{3} + 3^{4}$

Step 2

Simplify each term.

Multiply $3$ by $4$ .

$x^{4} + 12 x^{3} + 6 x^{2} \cdot 3^{2} + 4 x \cdot 3^{3} + 3^{4}$

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

$x^{4} + 12 x^{3} + 6 x^{2} \cdot 9 + 4 x \cdot 3^{3} + 3^{4}$

Multiply $9$ by $6$ .

$x^{4} + 12 x^{3} + 54 x^{2} + 4 x \cdot 3^{3} + 3^{4}$

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

$x^{4} + 12 x^{3} + 54 x^{2} + 4 x \cdot 27 + 3^{4}$

Multiply $27$ by $4$ .

$x^{4} + 12 x^{3} + 54 x^{2} + 108 x + 3^{4}$

Raise $3$ to the power of $4$ .

$x^{4} + 12 x^{3} + 54 x^{2} + 108 x + 81$