Algebra Examples

$\frac{56 y^{3} + 49 y^{2}}{- 7 y}$

Step 1

Simplify terms.

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Step 1.1

Factor $7 y^{2}$ out of $56 y^{3} + 49 y^{2}$ .

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Step 1.1.1

Factor $7 y^{2}$ out of $56 y^{3}$ .

$\frac{7 y^{2} (8 y) + 49 y^{2}}{- 7 y}$

Step 1.1.2

Factor $7 y^{2}$ out of $49 y^{2}$ .

$\frac{7 y^{2} (8 y) + 7 y^{2} (7)}{- 7 y}$

Step 1.1.3

Factor $7 y^{2}$ out of $7 y^{2} (8 y) + 7 y^{2} (7)$ .

$\frac{7 y^{2} (8 y + 7)}{- 7 y}$

Step 1.2

Cancel the common factor of $7$ and $- 7$ .

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Step 1.2.1

Factor $7$ out of $7 y^{2} (8 y + 7)$ .

$\frac{7 (y^{2} (8 y + 7))}{- 7 y}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $7$ out of $- 7 y$ .

$\frac{7 (y^{2} (8 y + 7))}{7 (- y)}$

Step 1.2.2.2

Cancel the common factor.

$\frac{7 (y^{2} (8 y + 7))}{7 (- y)}$

Step 1.2.2.3

Rewrite the expression.

$\frac{y^{2} (8 y + 7)}{- y}$

Step 1.3

Cancel the common factor of $y^{2}$ and $y$ .

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Step 1.3.1

Factor $y$ out of $y^{2} (8 y + 7)$ .

$\frac{y (y (8 y + 7))}{- y}$

Step 1.3.2

Move the negative one from the denominator of $\frac{y (8 y + 7)}{- 1}$ .

$- 1 \cdot (y (8 y + 7))$

Step 1.4

Rewrite $- 1 \cdot (y (8 y + 7))$ as $- (y (8 y + 7))$ .

$- (y (8 y + 7))$

Step 1.5

Apply the distributive property.

$- (y (8 y) + y \cdot 7)$

Step 1.6

Reorder.

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Step 1.6.1

Rewrite using the commutative property of multiplication.

$- (8 y \cdot y + y \cdot 7)$

Step 1.6.2

Move $7$ to the left of $y$ .

$- (8 y \cdot y + 7 \cdot y)$

Step 2

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

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Step 2.1

Move $y$ .

$- (8 (y \cdot y) + 7 \cdot y)$

Step 2.2

Multiply $y$ by $y$ .

$- (8 y^{2} + 7 \cdot y)$

$- (8 y^{2} + 7 y)$

Step 3

Simplify by multiplying through.

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Step 3.1

Apply the distributive property.

$- (8 y^{2}) - (7 y)$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $8$ by $- 1$ .

$- 8 y^{2} - (7 y)$

Step 3.2.2

Multiply $7$ by $- 1$ .

$- 8 y^{2} - 7 y$