Simplify (x^2+4)(x^2-4)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Combine the opposite terms in $x^{2} x^{2} + x^{2} \cdot - 4 + 4 x^{2} + 4 \cdot - 4$ .

Reorder the factors in the terms $x^{2} \cdot - 4$ and $4 x^{2}$ .

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

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

$x^{2} x^{2} + 0 + 4 \cdot - 4$

Add $x^{2} x^{2}$ and $0$ .

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

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.

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

Add $2$ and $2$ .

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

Multiply $4$ by $- 4$ .

$x^{4} - 16$