Basic Math Examples

$2 (y - 3) (y + 2) - (y - 4) (y + 4)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$(2 y + 2 \cdot - 3) (y + 2) - (y - 4) (y + 4)$

Step 1.2

Multiply $2$ by $- 3$ .

$(2 y - 6) (y + 2) - (y - 4) (y + 4)$

Step 1.3

Expand $(2 y - 6) (y + 2)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$2 y (y + 2) - 6 (y + 2) - (y - 4) (y + 4)$

Step 1.3.2

Apply the distributive property.

$2 y \cdot y + 2 y \cdot 2 - 6 (y + 2) - (y - 4) (y + 4)$

Step 1.3.3

Apply the distributive property.

$2 y \cdot y + 2 y \cdot 2 - 6 y - 6 \cdot 2 - (y - 4) (y + 4)$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $y$ by $y$ by adding the exponents.

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Step 1.4.1.1.1

Move $y$ .

$2 (y \cdot y) + 2 y \cdot 2 - 6 y - 6 \cdot 2 - (y - 4) (y + 4)$

Step 1.4.1.1.2

Multiply $y$ by $y$ .

$2 y^{2} + 2 y \cdot 2 - 6 y - 6 \cdot 2 - (y - 4) (y + 4)$

Step 1.4.1.2

Multiply $2$ by $2$ .

$2 y^{2} + 4 y - 6 y - 6 \cdot 2 - (y - 4) (y + 4)$

Step 1.4.1.3

Multiply $- 6$ by $2$ .

$2 y^{2} + 4 y - 6 y - 12 - (y - 4) (y + 4)$

Step 1.4.2

Subtract $6 y$ from $4 y$ .

$2 y^{2} - 2 y - 12 - (y - 4) (y + 4)$

Step 1.5

Apply the distributive property.

$2 y^{2} - 2 y - 12 + (- y - - 4) (y + 4)$

Step 1.6

Multiply $- 1$ by $- 4$ .

$2 y^{2} - 2 y - 12 + (- y + 4) (y + 4)$

Step 1.7

Expand $(- y + 4) (y + 4)$ using the FOIL Method.

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Step 1.7.1

Apply the distributive property.

$2 y^{2} - 2 y - 12 - y (y + 4) + 4 (y + 4)$

Step 1.7.2

Apply the distributive property.

$2 y^{2} - 2 y - 12 - y \cdot y - y \cdot 4 + 4 (y + 4)$

Step 1.7.3

Apply the distributive property.

$2 y^{2} - 2 y - 12 - y \cdot y - y \cdot 4 + 4 y + 4 \cdot 4$

Step 1.8

Simplify and combine like terms.

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Step 1.8.1

Simplify each term.

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Step 1.8.1.1

Multiply $y$ by $y$ by adding the exponents.

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Step 1.8.1.1.1

Move $y$ .

$2 y^{2} - 2 y - 12 - (y \cdot y) - y \cdot 4 + 4 y + 4 \cdot 4$

Step 1.8.1.1.2

Multiply $y$ by $y$ .

$2 y^{2} - 2 y - 12 - y^{2} - y \cdot 4 + 4 y + 4 \cdot 4$

Step 1.8.1.2

Multiply $4$ by $- 1$ .

$2 y^{2} - 2 y - 12 - y^{2} - 4 y + 4 y + 4 \cdot 4$

Step 1.8.1.3

Multiply $4$ by $4$ .

$2 y^{2} - 2 y - 12 - y^{2} - 4 y + 4 y + 16$

Step 1.8.2

Add $- 4 y$ and $4 y$ .

$2 y^{2} - 2 y - 12 - y^{2} + 0 + 16$

Step 1.8.3

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

$2 y^{2} - 2 y - 12 - y^{2} + 16$

Step 2

Simplify by adding terms.

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Step 2.1

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

$y^{2} - 2 y - 12 + 16$

Step 2.2

Add $- 12$ and $16$ .

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