Algebra Examples

$- 8 x {(- 5 x + 1)}^{\frac{3}{5}} - 7 {(- 5 x + 1)}^{\frac{8}{5}}$

Step 1

Factor $- {(- 5 x + 1)}^{\frac{3}{5}}$ out of $- 8 x {(- 5 x + 1)}^{\frac{3}{5}} - 7 {(- 5 x + 1)}^{\frac{8}{5}}$ .

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Step 1.1

Factor $- {(- 5 x + 1)}^{\frac{3}{5}}$ out of $- 8 x {(- 5 x + 1)}^{\frac{3}{5}}$ .

$- {(- 5 x + 1)}^{\frac{3}{5}} (8 x) - 7 {(- 5 x + 1)}^{\frac{8}{5}}$

Step 1.2

Factor $- {(- 5 x + 1)}^{\frac{3}{5}}$ out of $- 7 {(- 5 x + 1)}^{\frac{8}{5}}$ .

$- {(- 5 x + 1)}^{\frac{3}{5}} (8 x) - {(- 5 x + 1)}^{\frac{3}{5}} (7 {(- 5 x + 1)}^{\frac{5}{5}})$

Step 1.3

Factor $- {(- 5 x + 1)}^{\frac{3}{5}}$ out of $- {(- 5 x + 1)}^{\frac{3}{5}} (8 x) - {(- 5 x + 1)}^{\frac{3}{5}} (7 {(- 5 x + 1)}^{\frac{5}{5}})$ .

$- {(- 5 x + 1)}^{\frac{3}{5}} (8 x + 7 {(- 5 x + 1)}^{\frac{5}{5}})$

Step 2

Divide $5$ by $5$ .

$- {(- 5 x + 1)}^{\frac{3}{5}} (8 x + 7 {(- 5 x + 1)}^{1})$

Step 3

Simplify.

$- {(- 5 x + 1)}^{\frac{3}{5}} (8 x + 7 (- 5 x + 1))$

Step 4

Apply the distributive property.

$- {(- 5 x + 1)}^{\frac{3}{5}} (8 x + 7 (- 5 x) + 7 \cdot 1)$

Step 5

Multiply $- 5$ by $7$ .

$- {(- 5 x + 1)}^{\frac{3}{5}} (8 x - 35 x + 7 \cdot 1)$

Step 6

Multiply $7$ by $1$ .

$- {(- 5 x + 1)}^{\frac{3}{5}} (8 x - 35 x + 7)$

Step 7

Subtract $35 x$ from $8 x$ .

$- {(- 5 x + 1)}^{\frac{3}{5}} (- 27 x + 7)$

Step 8

Factor.

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Step 8.1

Factor $- 1$ out of $- 27 x + 7$ .

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Step 8.1.1

Factor $- 1$ out of $- 27 x$ .

$- {(- 5 x + 1)}^{\frac{3}{5}} (- (27 x) + 7)$

Step 8.1.2

Rewrite $7$ as $- 1 (- 7)$ .

$- {(- 5 x + 1)}^{\frac{3}{5}} (- (27 x) - 1 (- 7))$

Step 8.1.3

Factor $- 1$ out of $- (27 x) - 1 (- 7)$ .

$- {(- 5 x + 1)}^{\frac{3}{5}} (- (27 x - 7))$

Step 8.2

Remove unnecessary parentheses.

$- {(- 5 x + 1)}^{\frac{3}{5}} \cdot - 1 (27 x - 7)$

Step 9

Combine exponents.

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Step 9.1

Factor out negative.

$- ({(- 5 x + 1)}^{\frac{3}{5}} \cdot - 1 (27 x - 7))$

Step 9.2

Multiply $- 1$ by $- 1$ .

$1 ({(- 5 x + 1)}^{\frac{3}{5}} (27 x - 7))$

Step 9.3

Multiply ${(- 5 x + 1)}^{\frac{3}{5}}$ by $1$ .

${(- 5 x + 1)}^{\frac{3}{5}} (27 x - 7)$