Pre-Algebra Examples

$\frac{2 y^{5} + 9 y^{3} + 3 y^{2}}{- y^{2}}$

Step 1

Factor $y^{2}$ out of $2 y^{5} + 9 y^{3} + 3 y^{2}$ .

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Step 1.1

Factor $y^{2}$ out of $2 y^{5}$ .

$\frac{y^{2} (2 y^{3}) + 9 y^{3} + 3 y^{2}}{- y^{2}}$

Step 1.2

Factor $y^{2}$ out of $9 y^{3}$ .

$\frac{y^{2} (2 y^{3}) + y^{2} (9 y) + 3 y^{2}}{- y^{2}}$

Step 1.3

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

$\frac{y^{2} (2 y^{3}) + y^{2} (9 y) + y^{2} \cdot 3}{- y^{2}}$

Step 1.4

Factor $y^{2}$ out of $y^{2} (2 y^{3}) + y^{2} (9 y)$ .

$\frac{y^{2} (2 y^{3} + 9 y) + y^{2} \cdot 3}{- y^{2}}$

Step 1.5

Factor $y^{2}$ out of $y^{2} (2 y^{3} + 9 y) + y^{2} \cdot 3$ .

$\frac{y^{2} (2 y^{3} + 9 y + 3)}{- y^{2}}$

Step 2

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

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Step 2.1

Cancel the common factor.

$\frac{y^{2} (2 y^{3} + 9 y + 3)}{- y^{2}}$

Step 2.2

Rewrite the expression.

$\frac{2 y^{3} + 9 y + 3}{- 1}$

Step 2.3

Move the negative one from the denominator of $\frac{2 y^{3} + 9 y + 3}{- 1}$ .

$- 1 \cdot (2 y^{3} + 9 y + 3)$

Step 3

Rewrite $- 1 \cdot (2 y^{3} + 9 y + 3)$ as $- (2 y^{3} + 9 y + 3)$ .

$- (2 y^{3} + 9 y + 3)$

Step 4

Apply the distributive property.

$- (2 y^{3}) - (9 y) - 1 \cdot 3$

Step 5

Simplify.

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Step 5.1

Multiply $2$ by $- 1$ .

$- 2 y^{3} - (9 y) - 1 \cdot 3$

Step 5.2

Multiply $9$ by $- 1$ .

$- 2 y^{3} - 9 y - 1 \cdot 3$

Step 5.3

Multiply $- 1$ by $3$ .

$- 2 y^{3} - 9 y - 3$