Simplify (4y-8y^2)/(10y-5)

$\frac{4 y - 8 y^{2}}{10 y - 5}$

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

Factor $4 y$ out of $4 y$ .

$\frac{4 y (1) - 8 y^{2}}{10 y - 5}$

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

$\frac{4 y (1) + 4 y (- 2 y)}{10 y - 5}$

Factor $4 y$ out of $4 y (1) + 4 y (- 2 y)$ .

$\frac{4 y (1 - 2 y)}{10 y - 5}$

$\frac{4 y (1 - 2 y)}{10 y - 5}$

Factor $5$ out of $10 y - 5$ .

Factor $5$ out of $10 y$ .

$\frac{4 y (1 - 2 y)}{5 (2 y) - 5}$

Factor $5$ out of $- 5$ .

$\frac{4 y (1 - 2 y)}{5 (2 y) + 5 (- 1)}$

Factor $5$ out of $5 (2 y) + 5 (- 1)$ .

$\frac{4 y (1 - 2 y)}{5 (2 y - 1)}$

$\frac{4 y (1 - 2 y)}{5 (2 y - 1)}$

Cancel the common factor of $1 - 2 y$ and $2 y - 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{4 y (- 1 (- 1) - 2 y)}{5 (2 y - 1)}$

Factor $- 1$ out of $- 2 y$ .

$\frac{4 y (- 1 (- 1) - (2 y))}{5 (2 y - 1)}$

Factor $- 1$ out of $- 1 (- 1) - (2 y)$ .

$\frac{4 y (- 1 (- 1 + 2 y))}{5 (2 y - 1)}$

Reorder terms.

$\frac{4 y (- 1 (2 y - 1))}{5 (2 y - 1)}$

Cancel the common factor.

$\frac{4 y (- 1 (2 y - 1))}{5 (2 y - 1)}$

Rewrite the expression.

$\frac{4 y \cdot (- 1)}{5}$

$\frac{4 y \cdot (- 1)}{5}$

Simplify the expression.

Multiply $- 1$ by $4$ .

$\frac{- 4 y}{5}$

Move the negative in front of the fraction.

$- \frac{4 y}{5}$

$- \frac{4 y}{5}$

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