Algebra Examples

$\frac{(8 x - 56 x^{2})}{\sqrt{14 x - 2}}$

Step 1

Factor $8 x$ out of $8 x - 56 x^{2}$ .

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Step 1.1

Factor $8 x$ out of $8 x$ .

$\frac{8 x (1) - 56 x^{2}}{\sqrt{14 x - 2}}$

Step 1.2

Factor $8 x$ out of $- 56 x^{2}$ .

$\frac{8 x (1) + 8 x (- 7 x)}{\sqrt{14 x - 2}}$

Step 1.3

Factor $8 x$ out of $8 x (1) + 8 x (- 7 x)$ .

$\frac{8 x (1 - 7 x)}{\sqrt{14 x - 2}}$

Step 2

Factor $2$ out of $14 x - 2$ .

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Step 2.1

Factor $2$ out of $14 x$ .

$\frac{8 x (1 - 7 x)}{\sqrt{2 (7 x) - 2}}$

Step 2.2

Factor $2$ out of $- 2$ .

$\frac{8 x (1 - 7 x)}{\sqrt{2 (7 x) + 2 (- 1)}}$

Step 2.3

Factor $2$ out of $2 (7 x) + 2 (- 1)$ .

$\frac{8 x (1 - 7 x)}{\sqrt{2 (7 x - 1)}}$

Step 3

Multiply $\frac{8 x (1 - 7 x)}{\sqrt{2 (7 x - 1)}}$ by $\frac{\sqrt{2 (7 x - 1)}}{\sqrt{2 (7 x - 1)}}$ .

$\frac{8 x (1 - 7 x)}{\sqrt{2 (7 x - 1)}} \cdot \frac{\sqrt{2 (7 x - 1)}}{\sqrt{2 (7 x - 1)}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{8 x (1 - 7 x)}{\sqrt{2 (7 x - 1)}}$ by $\frac{\sqrt{2 (7 x - 1)}}{\sqrt{2 (7 x - 1)}}$ .

$\frac{8 x (1 - 7 x) \sqrt{2 (7 x - 1)}}{\sqrt{2 (7 x - 1)} \sqrt{2 (7 x - 1)}}$

Step 4.2

Raise $\sqrt{2 (7 x - 1)}$ to the power of $1$ .

$\frac{8 x (1 - 7 x) \sqrt{2 (7 x - 1)}}{{\sqrt{2 (7 x - 1)}}^{1} \sqrt{2 (7 x - 1)}}$

Step 4.3

Raise $\sqrt{2 (7 x - 1)}$ to the power of $1$ .

$\frac{8 x (1 - 7 x) \sqrt{2 (7 x - 1)}}{{\sqrt{2 (7 x - 1)}}^{1} {\sqrt{2 (7 x - 1)}}^{1}}$

Step 4.4

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

$\frac{8 x (1 - 7 x) \sqrt{2 (7 x - 1)}}{{\sqrt{2 (7 x - 1)}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$\frac{8 x (1 - 7 x) \sqrt{2 (7 x - 1)}}{{\sqrt{2 (7 x - 1)}}^{2}}$

Step 4.6

Rewrite ${\sqrt{2 (7 x - 1)}}^{2}$ as $2 (7 x - 1)$ .

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Step 4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 (7 x - 1)}$ as ${(2 (7 x - 1))}^{\frac{1}{2}}$ .

$\frac{8 x (1 - 7 x) \sqrt{2 (7 x - 1)}}{{({(2 (7 x - 1))}^{\frac{1}{2}})}^{2}}$

Step 4.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{8 x (1 - 7 x) \sqrt{2 (7 x - 1)}}{{(2 (7 x - 1))}^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{8 x (1 - 7 x) \sqrt{2 (7 x - 1)}}{{(2 (7 x - 1))}^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$\frac{8 x (1 - 7 x) \sqrt{2 (7 x - 1)}}{{(2 (7 x - 1))}^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$\frac{8 x (1 - 7 x) \sqrt{2 (7 x - 1)}}{{(2 (7 x - 1))}^{1}}$

Step 4.6.5

Simplify.

$\frac{8 x (1 - 7 x) \sqrt{2 (7 x - 1)}}{2 (7 x - 1)}$

Step 5

Cancel the common factor of $8$ and $2$ .

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Step 5.1

Factor $2$ out of $8 x (1 - 7 x) \sqrt{2 (7 x - 1)}$ .

$\frac{2 (4 x (1 - 7 x) \sqrt{2 (7 x - 1)})}{2 (7 x - 1)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Cancel the common factor.

$\frac{2 (4 x (1 - 7 x) \sqrt{2 (7 x - 1)})}{2 (7 x - 1)}$

Step 5.2.2

Rewrite the expression.

$\frac{4 x (1 - 7 x) \sqrt{2 (7 x - 1)}}{7 x - 1}$

Step 6

Cancel the common factor of $1 - 7 x$ and $7 x - 1$ .

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Step 6.1

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{4 x (- 1 (- 1) - 7 x) \sqrt{2 (7 x - 1)}}{7 x - 1}$

Step 6.2

Factor $- 1$ out of $- 7 x$ .

$\frac{4 x (- 1 (- 1) - (7 x)) \sqrt{2 (7 x - 1)}}{7 x - 1}$

Step 6.3

Factor $- 1$ out of $- 1 (- 1) - (7 x)$ .

$\frac{4 x (- 1 (- 1 + 7 x)) \sqrt{2 (7 x - 1)}}{7 x - 1}$

Step 6.4

Reorder terms.

$\frac{4 x (- 1 (7 x - 1)) \sqrt{2 (7 x - 1)}}{7 x - 1}$

Step 6.5

Cancel the common factor.

$\frac{4 x (- 1 (7 x - 1)) \sqrt{2 (7 x - 1)}}{7 x - 1}$

Step 6.6

Divide $4 x \cdot (- 1) \sqrt{2 (7 x - 1)}$ by $1$ .

$4 x \cdot (- 1) \sqrt{2 (7 x - 1)}$

Step 7

Multiply $- 1$ by $4$ .

$- 4 x \sqrt{2 (7 x - 1)}$