Basic Math Examples

$(x^{2} + 7) (x^{2} - 7)$

Step 1

Expand $(x^{2} + 7) (x^{2} - 7)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$x^{2} (x^{2} - 7) + 7 (x^{2} - 7)$

Step 1.2

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot - 7 + 7 (x^{2} - 7)$

Step 1.3

Apply the distributive property.

$x^{2} x^{2} + x^{2} \cdot - 7 + 7 x^{2} + 7 \cdot - 7$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $x^{2} x^{2} + x^{2} \cdot - 7 + 7 x^{2} + 7 \cdot - 7$ .

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Step 2.1.1

Reorder the factors in the terms $x^{2} \cdot - 7$ and $7 x^{2}$ .

$x^{2} x^{2} - 7 x^{2} + 7 x^{2} + 7 \cdot - 7$

Step 2.1.2

Add $- 7 x^{2}$ and $7 x^{2}$ .

$x^{2} x^{2} + 0 + 7 \cdot - 7$

Step 2.1.3

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

$x^{2} x^{2} + 7 \cdot - 7$

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.

$x^{2 + 2} + 7 \cdot - 7$

Step 2.2.1.2

Add $2$ and $2$ .

$x^{4} + 7 \cdot - 7$

Step 2.2.2

Multiply $7$ by $- 7$ .

$x^{4} - 49$