Evaluate (x^2+4)^2+4

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

Simplify each term.

Rewrite ${(x^{2} + 4)}^{2}$ as $(x^{2} + 4) (x^{2} + 4)$ .

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

Expand $(x^{2} + 4) (x^{2} + 4)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

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

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

Add $2$ and $2$ .

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

Move $4$ to the left of $x^{2}$ .

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

Multiply $4$ by $4$ .

$x^{4} + 4 x^{2} + 4 x^{2} + 16 + 4$

Add $4 x^{2}$ and $4 x^{2}$ .

$x^{4} + 8 x^{2} + 16 + 4$

Add $16$ and $4$ .

$x^{4} + 8 x^{2} + 20$