Basic Math Examples

$8 y - \frac{8}{(2 y - 2) (4 y + 8)}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $8$ and $2 y - 2$ .

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Step 1.1.1

Factor $2$ out of $8$ .

$8 y - \frac{2 (4)}{(2 y - 2) (4 y + 8)}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $(2 y - 2) (4 y + 8)$ .

$8 y - \frac{2 (4)}{2 ((y - 1) (4 y + 8))}$

Step 1.1.2.2

Cancel the common factor.

$8 y - \frac{2 \cdot 4}{2 ((y - 1) (4 y + 8))}$

Step 1.1.2.3

Rewrite the expression.

$8 y - \frac{4}{(y - 1) (4 y + 8)}$

Step 1.2

Cancel the common factor of $4$ and $4 y + 8$ .

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Step 1.2.1

Factor $4$ out of $4$ .

$8 y - \frac{4 \cdot 1}{(y - 1) (4 y + 8)}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $4$ out of $(y - 1) (4 y + 8)$ .

$8 y - \frac{4 \cdot 1}{4 ((y - 1) (y + 2))}$

Step 1.2.2.2

Cancel the common factor.

$8 y - \frac{4 \cdot 1}{4 ((y - 1) (y + 2))}$

Step 1.2.2.3

Rewrite the expression.

$8 y - \frac{1}{(y - 1) (y + 2)}$

Step 2

To write $8 y$ as a fraction with a common denominator, multiply by $\frac{(y - 1) (y + 2)}{(y - 1) (y + 2)}$ .

$8 y \cdot \frac{(y - 1) (y + 2)}{(y - 1) (y + 2)} - \frac{1}{(y - 1) (y + 2)}$

Step 3

Simplify terms.

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Step 3.1

Combine $8 y$ and $\frac{(y - 1) (y + 2)}{(y - 1) (y + 2)}$ .

$\frac{8 y ((y - 1) (y + 2))}{(y - 1) (y + 2)} - \frac{1}{(y - 1) (y + 2)}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{8 y ((y - 1) (y + 2)) - 1}{(y - 1) (y + 2)}$

Step 4

Simplify the numerator.

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Step 4.1

Expand $(y - 1) (y + 2)$ using the FOIL Method.

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Step 4.1.1

Apply the distributive property.

$\frac{8 y (y (y + 2) - 1 (y + 2)) - 1}{(y - 1) (y + 2)}$

Step 4.1.2

Apply the distributive property.

$\frac{8 y (y \cdot y + y \cdot 2 - 1 (y + 2)) - 1}{(y - 1) (y + 2)}$

Step 4.1.3

Apply the distributive property.

$\frac{8 y (y \cdot y + y \cdot 2 - 1 y - 1 \cdot 2) - 1}{(y - 1) (y + 2)}$

Step 4.2

Simplify and combine like terms.

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

Multiply $y$ by $y$ .

$\frac{8 y (y^{2} + y \cdot 2 - 1 y - 1 \cdot 2) - 1}{(y - 1) (y + 2)}$

Step 4.2.1.2

Move $2$ to the left of $y$ .

$\frac{8 y (y^{2} + 2 \cdot y - 1 y - 1 \cdot 2) - 1}{(y - 1) (y + 2)}$

Step 4.2.1.3

Rewrite $- 1 y$ as $- y$ .

$\frac{8 y (y^{2} + 2 y - y - 1 \cdot 2) - 1}{(y - 1) (y + 2)}$

Step 4.2.1.4

Multiply $- 1$ by $2$ .

$\frac{8 y (y^{2} + 2 y - y - 2) - 1}{(y - 1) (y + 2)}$

Step 4.2.2

Subtract $y$ from $2 y$ .

$\frac{8 y (y^{2} + y - 2) - 1}{(y - 1) (y + 2)}$

Step 4.3

Apply the distributive property.

$\frac{8 y \cdot y^{2} + 8 y \cdot y + 8 y \cdot - 2 - 1}{(y - 1) (y + 2)}$

Step 4.4

Simplify.

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Step 4.4.1

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

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Step 4.4.1.1

Move $y^{2}$ .

$\frac{8 (y^{2} y) + 8 y \cdot y + 8 y \cdot - 2 - 1}{(y - 1) (y + 2)}$

Step 4.4.1.2

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

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Step 4.4.1.2.1

Raise $y$ to the power of $1$ .

$\frac{8 (y^{2} y^{1}) + 8 y \cdot y + 8 y \cdot - 2 - 1}{(y - 1) (y + 2)}$

Step 4.4.1.2.2

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

$\frac{8 y^{2 + 1} + 8 y \cdot y + 8 y \cdot - 2 - 1}{(y - 1) (y + 2)}$

Step 4.4.1.3

Add $2$ and $1$ .

$\frac{8 y^{3} + 8 y \cdot y + 8 y \cdot - 2 - 1}{(y - 1) (y + 2)}$

Step 4.4.2

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

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Step 4.4.2.1

Move $y$ .

$\frac{8 y^{3} + 8 (y \cdot y) + 8 y \cdot - 2 - 1}{(y - 1) (y + 2)}$

Step 4.4.2.2

Multiply $y$ by $y$ .

$\frac{8 y^{3} + 8 y^{2} + 8 y \cdot - 2 - 1}{(y - 1) (y + 2)}$

Step 4.4.3

Multiply $- 2$ by $8$ .

$\frac{8 y^{3} + 8 y^{2} - 16 y - 1}{(y - 1) (y + 2)}$