Algebra Examples

$\frac{10 b^{2} + 70 b}{8 b - 24} \cdot \frac{8 b - 24}{10 b^{2} + 40 b}$

Step 1

Factor $10 b$ out of $10 b^{2} + 70 b$ .

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Step 1.1

Factor $10 b$ out of $10 b^{2}$ .

$\frac{10 b (b) + 70 b}{8 b - 24} \cdot \frac{8 b - 24}{10 b^{2} + 40 b}$

Step 1.2

Factor $10 b$ out of $70 b$ .

$\frac{10 b (b) + 10 b (7)}{8 b - 24} \cdot \frac{8 b - 24}{10 b^{2} + 40 b}$

Step 1.3

Factor $10 b$ out of $10 b (b) + 10 b (7)$ .

$\frac{10 b (b + 7)}{8 b - 24} \cdot \frac{8 b - 24}{10 b^{2} + 40 b}$

Step 2

Factor $8$ out of $8 b - 24$ .

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Step 2.1

Factor $8$ out of $8 b$ .

$\frac{10 b (b + 7)}{8 (b) - 24} \cdot \frac{8 b - 24}{10 b^{2} + 40 b}$

Step 2.2

Factor $8$ out of $- 24$ .

$\frac{10 b (b + 7)}{8 b + 8 \cdot - 3} \cdot \frac{8 b - 24}{10 b^{2} + 40 b}$

Step 2.3

Factor $8$ out of $8 b + 8 \cdot - 3$ .

$\frac{10 b (b + 7)}{8 (b - 3)} \cdot \frac{8 b - 24}{10 b^{2} + 40 b}$

Step 3

Factor $8$ out of $8 b - 24$ .

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Step 3.1

Factor $8$ out of $8 b$ .

$\frac{10 b (b + 7)}{8 (b - 3)} \cdot \frac{8 (b) - 24}{10 b^{2} + 40 b}$

Step 3.2

Factor $8$ out of $- 24$ .

$\frac{10 b (b + 7)}{8 (b - 3)} \cdot \frac{8 b + 8 \cdot - 3}{10 b^{2} + 40 b}$

Step 3.3

Factor $8$ out of $8 b + 8 \cdot - 3$ .

$\frac{10 b (b + 7)}{8 (b - 3)} \cdot \frac{8 (b - 3)}{10 b^{2} + 40 b}$

Step 4

Factor $10 b$ out of $10 b^{2} + 40 b$ .

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Step 4.1

Factor $10 b$ out of $10 b^{2}$ .

$\frac{10 b (b + 7)}{8 (b - 3)} \cdot \frac{8 (b - 3)}{10 b (b) + 40 b}$

Step 4.2

Factor $10 b$ out of $40 b$ .

$\frac{10 b (b + 7)}{8 (b - 3)} \cdot \frac{8 (b - 3)}{10 b (b) + 10 b (4)}$

Step 4.3

Factor $10 b$ out of $10 b (b) + 10 b (4)$ .

$\frac{10 b (b + 7)}{8 (b - 3)} \cdot \frac{8 (b - 3)}{10 b (b + 4)}$

Step 5

Cancel the common factor of $10 b$ .

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Step 5.1

Cancel the common factor.

$\frac{10 b (b + 7)}{8 (b - 3)} \cdot \frac{8 (b - 3)}{10 b (b + 4)}$

Step 5.2

Rewrite the expression.

$\frac{b + 7}{8 (b - 3)} \cdot \frac{8 (b - 3)}{b + 4}$

Step 6

Cancel the common factor of $8 (b - 3)$ .

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Step 6.1

Cancel the common factor.

$\frac{b + 7}{8 (b - 3)} \cdot \frac{8 (b - 3)}{b + 4}$

Step 6.2

Rewrite the expression.

$(b + 7) \cdot \frac{1}{b + 4}$

Step 7

Multiply $b + 7$ by $\frac{1}{b + 4}$ .

$\frac{b + 7}{b + 4}$