Basic Math Examples

$(y^{2} + 12) (y^{2} - 12)$

Step 1

Expand $(y^{2} + 12) (y^{2} - 12)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$y^{2} (y^{2} - 12) + 12 (y^{2} - 12)$

Step 1.2

Apply the distributive property.

$y^{2} y^{2} + y^{2} \cdot - 12 + 12 (y^{2} - 12)$

Step 1.3

Apply the distributive property.

$y^{2} y^{2} + y^{2} \cdot - 12 + 12 y^{2} + 12 \cdot - 12$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $y^{2} y^{2} + y^{2} \cdot - 12 + 12 y^{2} + 12 \cdot - 12$ .

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Step 2.1.1

Reorder the factors in the terms $y^{2} \cdot - 12$ and $12 y^{2}$ .

$y^{2} y^{2} - 12 y^{2} + 12 y^{2} + 12 \cdot - 12$

Step 2.1.2

Add $- 12 y^{2}$ and $12 y^{2}$ .

$y^{2} y^{2} + 0 + 12 \cdot - 12$

Step 2.1.3

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

$y^{2} y^{2} + 12 \cdot - 12$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $y^{2}$ by $y^{2}$ 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.

$y^{2 + 2} + 12 \cdot - 12$

Step 2.2.1.2

Add $2$ and $2$ .

$y^{4} + 12 \cdot - 12$

Step 2.2.2

Multiply $12$ by $- 12$ .

$y^{4} - 144$