Simplify 8y^2-4y+1÷2y-1

$8 y^{2} - 4 y + 1 \div 2 y - 1$

Rewrite the division as a fraction.

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

To write $8 y^{2}$ as a fraction with a common denominator, multiply by $\frac{2 y}{2 y}$ .

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

Simplify terms.

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Combine $8 y^{2}$ and $\frac{2 y}{2 y}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Rewrite using the commutative property of multiplication.

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

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

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

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

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

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

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

Add $2$ and $1$ .

$- 4 y + \frac{8 \cdot 2 y^{3} + 1}{2 y} - 1$

Multiply $8$ by $2$ .

$- 4 y + \frac{16 y^{3} + 1}{2 y} - 1$

To write $- 4 y$ as a fraction with a common denominator, multiply by $\frac{2 y}{2 y}$ .

$- 4 y \cdot \frac{2 y}{2 y} + \frac{16 y^{3} + 1}{2 y} - 1$

Simplify terms.

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Combine $- 4 y$ and $\frac{2 y}{2 y}$ .

$\frac{- 4 y (2 y)}{2 y} + \frac{16 y^{3} + 1}{2 y} - 1$

Combine the numerators over the common denominator.

$\frac{- 4 y (2 y) + 16 y^{3} + 1}{2 y} - 1$

Simplify the numerator.

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Multiply $y$ by $y$ .

$\frac{- 4 \cdot 2 y^{2} + 16 y^{3} + 1}{2 y} - 1$

Multiply $- 4$ by $2$ .

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

Reorder terms.

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

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

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

Simplify terms.

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Combine $- 1$ and $\frac{2 y}{2 y}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Reorder terms.

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

Factor out the greatest common factor from each group.

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Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $2 y - 1$ .

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

Simplify 8y^2-4y+1÷2y-1

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