Evaluate (1+x^2)^2

${(1 + x^{2})}^{2}$

Rewrite ${(1 + x^{2})}^{2}$ as $(1 + x^{2}) (1 + x^{2})$ .

$(1 + x^{2}) (1 + x^{2})$

Expand $(1 + x^{2}) (1 + x^{2})$ using the FOIL Method.

Apply the distributive property.

$1 (1 + x^{2}) + x^{2} (1 + x^{2})$

Apply the distributive property.

$1 \cdot 1 + 1 x^{2} + x^{2} (1 + x^{2})$

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

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

Multiply $x^{2}$ by $1$ .

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

Multiply $x^{2}$ by $1$ .

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

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

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

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

Add $2$ and $2$ .

$1 + x^{2} + x^{2} + x^{4}$

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

$1 + 2 x^{2} + x^{4}$