Algebra Examples

$\frac{2 a^{2} + 6}{5 b^{3}} \cdot \frac{10 b^{4}}{3 a^{2} + 9}$

Step 1

Factor $2$ out of $2 a^{2} + 6$ .

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Step 1.1

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

$\frac{2 (a^{2}) + 6}{5 b^{3}} \cdot \frac{10 b^{4}}{3 a^{2} + 9}$

Step 1.2

Factor $2$ out of $6$ .

$\frac{2 a^{2} + 2 \cdot 3}{5 b^{3}} \cdot \frac{10 b^{4}}{3 a^{2} + 9}$

Step 1.3

Factor $2$ out of $2 a^{2} + 2 \cdot 3$ .

$\frac{2 (a^{2} + 3)}{5 b^{3}} \cdot \frac{10 b^{4}}{3 a^{2} + 9}$

Step 2

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

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Step 2.1

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

$\frac{2 (a^{2} + 3)}{5 b^{3}} \cdot \frac{10 b^{4}}{3 (a^{2}) + 9}$

Step 2.2

Factor $3$ out of $9$ .

$\frac{2 (a^{2} + 3)}{5 b^{3}} \cdot \frac{10 b^{4}}{3 a^{2} + 3 \cdot 3}$

Step 2.3

Factor $3$ out of $3 a^{2} + 3 \cdot 3$ .

$\frac{2 (a^{2} + 3)}{5 b^{3}} \cdot \frac{10 b^{4}}{3 (a^{2} + 3)}$

Step 3

Combine.

$\frac{2 (a^{2} + 3) (10 b^{4})}{5 b^{3} (3 (a^{2} + 3))}$

Step 4

Cancel the common factor of $a^{2} + 3$ .

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Step 4.1

Cancel the common factor.

$\frac{2 (a^{2} + 3) (10 b^{4})}{5 b^{3} (3 (a^{2} + 3))}$

Step 4.2

Rewrite the expression.

$\frac{2 (10 b^{4})}{5 b^{3} \cdot (3)}$

Step 5

Cancel the common factor of $10$ and $5$ .

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Step 5.1

Factor $5$ out of $2 (10 b^{4})$ .

$\frac{5 (2 (2 b^{4}))}{5 b^{3} \cdot (3)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $5 b^{3} \cdot (3)$ .

$\frac{5 (2 (2 b^{4}))}{5 (b^{3} \cdot (3))}$

Step 5.2.2

Cancel the common factor.

$\frac{5 (2 (2 b^{4}))}{5 (b^{3} \cdot (3))}$

Step 5.2.3

Rewrite the expression.

$\frac{2 (2 b^{4})}{b^{3} \cdot (3)}$

Step 6

Cancel the common factor of $b^{4}$ and $b^{3}$ .

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Step 6.1

Factor $b^{3}$ out of $2 (2 b^{4})$ .

$\frac{b^{3} (2 (2 b))}{b^{3} \cdot (3)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $b^{3}$ out of $b^{3} \cdot (3)$ .

$\frac{b^{3} (2 (2 b))}{b^{3} (3)}$

Step 6.2.2

Cancel the common factor.

$\frac{b^{3} (2 (2 b))}{b^{3} \cdot 3}$

Step 6.2.3

Rewrite the expression.

$\frac{2 (2 b)}{3}$

Step 7

Multiply $2$ by $2$ .

$\frac{4 b}{3}$