Evaluate (4-x^2)^2

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 + 4 (- x^{2}) - x^{2} \cdot 4 - x^{2} (- x^{2})$

Multiply $- 1$ by $4$ .

$16 - 4 x^{2} - x^{2} \cdot 4 - x^{2} (- x^{2})$

Multiply $4$ by $- 1$ .

$16 - 4 x^{2} - 4 x^{2} - x^{2} (- x^{2})$

Rewrite using the commutative property of multiplication.

$16 - 4 x^{2} - 4 x^{2} - 1 \cdot - 1 x^{2} x^{2}$

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

Move $x^{2}$ .

$16 - 4 x^{2} - 4 x^{2} - 1 \cdot - 1 (x^{2} x^{2})$

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

$16 - 4 x^{2} - 4 x^{2} - 1 \cdot - 1 x^{2 + 2}$

Add $2$ and $2$ .

$16 - 4 x^{2} - 4 x^{2} - 1 \cdot - 1 x^{4}$

Multiply $- 1$ by $- 1$ .

$16 - 4 x^{2} - 4 x^{2} + 1 x^{4}$

Multiply $x^{4}$ by $1$ .

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

Subtract $4 x^{2}$ from $- 4 x^{2}$ .

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