Algebra Examples

$\frac{y^{3} + 5 y^{2}}{21 y^{3}} \cdot \frac{9 y^{3}}{y + 5}$

Step 1

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

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Step 1.1

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

$\frac{y^{2} y + 5 y^{2}}{21 y^{3}} \cdot \frac{9 y^{3}}{y + 5}$

Step 1.2

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

$\frac{y^{2} y + y^{2} \cdot 5}{21 y^{3}} \cdot \frac{9 y^{3}}{y + 5}$

Step 1.3

Factor $y^{2}$ out of $y^{2} y + y^{2} \cdot 5$ .

$\frac{y^{2} (y + 5)}{21 y^{3}} \cdot \frac{9 y^{3}}{y + 5}$

Step 2

Cancel the common factor of $y + 5$ .

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Step 2.1

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

$\frac{(y + 5) y^{2}}{21 y^{3}} \cdot \frac{9 y^{3}}{y + 5}$

Step 2.2

Cancel the common factor.

$\frac{(y + 5) y^{2}}{21 y^{3}} \cdot \frac{9 y^{3}}{y + 5}$

Step 2.3

Rewrite the expression.

$\frac{y^{2}}{21 y^{3}} \cdot (9 y^{3})$

Step 3

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

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Step 3.1

Factor $3 y^{3}$ out of $21 y^{3}$ .

$\frac{y^{2}}{3 y^{3} (7)} \cdot (9 y^{3})$

Step 3.2

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

$\frac{y^{2}}{3 y^{3} (7)} \cdot (3 y^{3} (3))$

Step 3.3

Cancel the common factor.

$\frac{y^{2}}{3 y^{3} \cdot 7} \cdot (3 y^{3} \cdot 3)$

Step 3.4

Rewrite the expression.

$\frac{y^{2}}{7} \cdot 3$

Step 4

Combine $\frac{y^{2}}{7}$ and $3$ .

$\frac{y^{2} \cdot 3}{7}$

Step 5

Move $3$ to the left of $y^{2}$ .

$\frac{3 y^{2}}{7}$