Basic Math Examples

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

Step 1

Expand $(y + 2) (y - 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $y \cdot y + y \cdot - 2 + 2 y + 2 \cdot - 2$ .

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Step 2.1.1

Reorder the factors in the terms $y \cdot - 2$ and $2 y$ .

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

Step 2.1.2

Add $- 2 y$ and $2 y$ .

$(y \cdot y + 0 + 2 \cdot - 2) (y^{2} + 4)$

Step 2.1.3

Add $y \cdot y$ and $0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $y$ by $y$ .

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

Step 2.2.2

Multiply $2$ by $- 2$ .

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

Step 3

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

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Step 3.1

Apply the distributive property.

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Apply the distributive property.

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

Step 4

Simplify terms.

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Step 4.1

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

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Step 4.1.1

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

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

Step 4.1.2

Subtract $4 y^{2}$ from $4 y^{2}$ .

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

Step 4.1.3

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

$y^{2} y^{2} - 4 \cdot 4$

Step 4.2

Simplify each term.

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Step 4.2.1

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

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Step 4.2.1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 4.2.1.2

Add $2$ and $2$ .

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

Step 4.2.2

Multiply $- 4$ by $4$ .

$y^{4} - 16$