Finite Math Examples

$\frac{5 y^{4} + 9 y^{3}}{- y^{2}}$

Step 1

Simplify terms.

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Step 1.1

Factor $y^{3}$ out of $5 y^{4} + 9 y^{3}$ .

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Step 1.1.1

Factor $y^{3}$ out of $5 y^{4}$ .

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

Step 1.1.2

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

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

Step 1.1.3

Factor $y^{3}$ out of $y^{3} (5 y) + y^{3} \cdot 9$ .

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

Step 1.2

Cancel the common factor of $y^{3}$ and $y^{2}$ .

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Step 1.2.1

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

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

Step 1.2.2

Move the negative one from the denominator of $\frac{y (5 y + 9)}{- 1}$ .

$- 1 \cdot (y (5 y + 9))$

Step 1.3

Rewrite $- 1 \cdot (y (5 y + 9))$ as $- (y (5 y + 9))$ .

$- (y (5 y + 9))$

Step 1.4

Apply the distributive property.

$- (y (5 y) + y \cdot 9)$

Step 1.5

Reorder.

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Step 1.5.1

Rewrite using the commutative property of multiplication.

$- (5 y \cdot y + y \cdot 9)$

Step 1.5.2

Move $9$ to the left of $y$ .

$- (5 y \cdot y + 9 \cdot y)$

Step 2

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

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Step 2.1

Move $y$ .

$- (5 (y \cdot y) + 9 \cdot y)$

Step 2.2

Multiply $y$ by $y$ .

$- (5 y^{2} + 9 \cdot y)$

$- (5 y^{2} + 9 y)$

Step 3

Simplify by multiplying through.

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Step 3.1

Apply the distributive property.

$- (5 y^{2}) - (9 y)$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $5$ by $- 1$ .

$- 5 y^{2} - (9 y)$

Step 3.2.2

Multiply $9$ by $- 1$ .

$- 5 y^{2} - 9 y$