Algebra Examples

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

Step 1

Expand

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

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

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Step 2.1.1

Reorder the factors in the terms

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

$4 x^{2}$ .

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

Step 2.1.2

Add

$- 4 x^{2}$ and

$4 x^{2}$ .

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

Step 2.1.3

Add

$x^{2} x^{2}$ and

$0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply

$x^{2}$ by

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

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Step 2.2.1.1

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.2.1.2

Add

$2$ and

$2$ .

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

Step 2.2.2

Multiply

$4$ by

$- 4$ .

$x^{4} - 16$

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

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