Evaluate (x+2)^4

${(x + 2)}^{4}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Multiply $2$ by $4$ .

$x^{4} + 8 x^{3} + 6 x^{2} \cdot 2^{2} + 4 x \cdot 2^{3} + 2^{4}$

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

$x^{4} + 8 x^{3} + 6 x^{2} \cdot 4 + 4 x \cdot 2^{3} + 2^{4}$

Multiply $4$ by $6$ .

$x^{4} + 8 x^{3} + 24 x^{2} + 4 x \cdot 2^{3} + 2^{4}$

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

$x^{4} + 8 x^{3} + 24 x^{2} + 4 x \cdot 8 + 2^{4}$

Multiply $8$ by $4$ .

$x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 2^{4}$

Raise $2$ to the power of $4$ .

$x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16$