Algebra Examples

$(56 y^{3} + 49 y^{2}) \div (- 7 y) y^{3}$

Step 1

Rewrite the division as a fraction.

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

Step 2

Multiply $y$ by $y^{3}$ by adding the exponents.

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Step 2.1

Move $y^{3}$ .

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

Step 2.2

Multiply $y^{3}$ by $y$ .

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Step 2.2.1

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

$\frac{56 y^{3} + 49 y^{2}}{- 7 (y^{3} y^{1})}$

Step 2.2.2

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

$\frac{56 y^{3} + 49 y^{2}}{- 7 y^{3 + 1}}$

Step 2.3

Add $3$ and $1$ .

$\frac{56 y^{3} + 49 y^{2}}{- 7 y^{4}}$

Step 3

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

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Step 3.1

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

$\frac{7 y^{2} (8 y) + 49 y^{2}}{- 7 y^{4}}$

Step 3.2

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

$\frac{7 y^{2} (8 y) + 7 y^{2} (7)}{- 7 y^{4}}$

Step 3.3

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

$\frac{7 y^{2} (8 y + 7)}{- 7 y^{4}}$

Step 4

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

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Step 4.1

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

$\frac{7 (y^{2} (8 y + 7))}{- 7 y^{4}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $7$ out of $- 7 y^{4}$ .

$\frac{7 (y^{2} (8 y + 7))}{7 (- y^{4})}$

Step 4.2.2

Cancel the common factor.

$\frac{7 (y^{2} (8 y + 7))}{7 (- y^{4})}$

Step 4.2.3

Rewrite the expression.

$\frac{y^{2} (8 y + 7)}{- y^{4}}$

Step 5

Cancel the common factors.

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Step 5.1

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

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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

Step 6

Move the negative in front of the fraction.

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

Step 7

Split the fraction $\frac{8 y + 7}{y^{2}}$ into two fractions.

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

Step 8

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

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Step 8.1

Factor $y$ out of $8 y$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

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

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

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