Basic Math Examples

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

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

Step 1

Simplify each term.

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Step 1.1

Rewrite

{(y - 2)}^{2}

${(y - 2)}^{2}$ as

(y - 2) (y - 2)

$(y - 2) (y - 2)$ .

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

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

Step 1.2

Expand

(y - 2) (y - 2)

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

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Step 1.2.1

Apply the distributive property.

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

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

Step 1.2.2

Apply the distributive property.

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

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

Step 1.2.3

Apply the distributive property.

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

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

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

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

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply

y

$y$ by

y

$y$ .

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

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

Step 1.3.1.2

Move

$- 2$ to the left of

$y$ .

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

Step 1.3.1.3

Multiply

$- 2$ by

$- 2$ .

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

Step 1.3.2

Subtract

$2 y$ from

$- 2 y$ .

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

Step 1.4

Rewrite

${(y + 2)}^{2}$ as

$(y + 2) (y + 2)$ .

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

Step 1.5

Expand

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

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Step 1.5.1

Apply the distributive property.

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

Step 1.5.2

Apply the distributive property.

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

Step 1.5.3

Apply the distributive property.

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

Step 1.6

Simplify and combine like terms.

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Step 1.6.1

Simplify each term.

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Step 1.6.1.1

Multiply

$y$ by

$y$ .

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

Step 1.6.1.2

Move

$2$ to the left of

$y$ .

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

Step 1.6.1.3

Multiply

$2$ by

$2$ .

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

Step 1.6.2

Add

$2 y$ and

$2 y$ .

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

Step 1.7

Apply the distributive property.

$y^{2} - 4 y + 4 - y^{2} - (4 y) - 1 \cdot 4$

Step 1.8

Simplify.

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Step 1.8.1

Multiply

$4$ by

$- 1$ .

$y^{2} - 4 y + 4 - y^{2} - 4 y - 1 \cdot 4$

Step 1.8.2

Multiply

$- 1$ by

$4$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in

$y^{2} - 4 y + 4 - y^{2} - 4 y - 4$ .

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Step 2.1.1

Subtract

$y^{2}$ from

$y^{2}$ .

$- 4 y + 4 + 0 - 4 y - 4$

Step 2.1.2

Add

$- 4 y + 4$ and

$0$ .

$- 4 y + 4 - 4 y - 4$

Step 2.1.3

Subtract

$4$ from

$4$ .

$- 4 y - 4 y + 0$

Step 2.1.4

Add

$- 4 y - 4 y$ and

$0$ .

$- 4 y - 4 y$

Step 2.2

Subtract

$4 y$ from

$- 4 y$ .

$- 8 y$