Simplify (x^2+5)(x^2-5)

$(x^{2} + 5) (x^{2} - 5)$

Step 1

Expand $(x^{2} + 5) (x^{2} - 5)$ using the FOIL Method.

Apply the distributive property.

$x^{2} (x^{2} - 5) + 5 (x^{2} - 5)$

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot - 5 + 5 (x^{2} - 5)$

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot - 5 + 5 x^{2} + 5 \cdot - 5$

Step 2

Simplify terms.

Combine the opposite terms in $x^{2} x^{2} + x^{2} \cdot - 5 + 5 x^{2} + 5 \cdot - 5$ .

Reorder the factors in the terms $x^{2} \cdot - 5$ and $5 x^{2}$ .

$x^{2} x^{2} - 5 x^{2} + 5 x^{2} + 5 \cdot - 5$

Add $- 5 x^{2}$ and $5 x^{2}$ .

$x^{2} x^{2} + 0 + 5 \cdot - 5$

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

$x^{2} x^{2} + 5 \cdot - 5$

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.

$x^{2 + 2} + 5 \cdot - 5$

Add $2$ and $2$ .

$x^{4} + 5 \cdot - 5$

Multiply $5$ by $- 5$ .

$x^{4} - 25$