Evaluate (x^2+2)^2

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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.

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

Add $2$ and $2$ .

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

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

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

Multiply $2$ by $2$ .

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

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

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