Simplify (8y^2-32)/(4y^2-16)

$\frac{8 y^{2} - 32}{4 y^{2} - 16}$

Step 1

Cancel the common factor of $8 y^{2} - 32$ and $4 y^{2} - 16$ .

Factor $4$ out of $8 y^{2}$ .

$\frac{4 (2 y^{2}) - 32}{4 y^{2} - 16}$

Factor $4$ out of $- 32$ .

$\frac{4 (2 y^{2}) + 4 \cdot - 8}{4 y^{2} - 16}$

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

$\frac{4 (2 y^{2} - 8)}{4 y^{2} - 16}$

Cancel the common factors.

Factor $4$ out of $4 y^{2}$ .

$\frac{4 (2 y^{2} - 8)}{4 (y^{2}) - 16}$

Factor $4$ out of $- 16$ .

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

Factor $4$ out of $4 y^{2} + 4 \cdot - 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 y^{2} - 8}{y^{2} - 4}$

Step 2

Simplify the numerator.

Factor $2$ out of $2 y^{2} - 8$ .

Factor $2$ out of $2 y^{2}$ .

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

Factor $2$ out of $- 8$ .

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

Factor $2$ out of $2 y^{2} + 2 \cdot - 4$ .

$\frac{2 (y^{2} - 4)}{y^{2} - 4}$

Rewrite $4$ as $2^{2}$ .

$\frac{2 (y^{2} - 2^{2})}{y^{2} - 4}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 2$ .

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

Step 3

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 2$ .

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

Step 4

Reduce the expression by cancelling the common factors.

Cancel the common factor of $y + 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 (y - 2)}{y - 2}$

Cancel the common factor of $y - 2$ .

Cancel the common factor.

$\frac{2 (y - 2)}{y - 2}$

Divide $2$ by $1$ .

$2$

Simplify (8y^2-32)/(4y^2-16)

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