Factor (x+8)^(1/3)-(x+8)^(4/3)

${(x + 8)}^{\frac{1}{3}} - {(x + 8)}^{\frac{4}{3}}$

Factor ${(x + 8)}^{\frac{1}{3}}$ out of ${(x + 8)}^{\frac{1}{3}} - {(x + 8)}^{\frac{4}{3}}$ .

Multiply by $1$ .

${(x + 8)}^{\frac{1}{3}} \cdot 1 - {(x + 8)}^{\frac{4}{3}}$

Factor ${(x + 8)}^{\frac{1}{3}}$ out of $- {(x + 8)}^{\frac{4}{3}}$ .

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

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

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

Rewrite $1$ as $1^{3}$ .

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

Rewrite ${(x + 8)}^{\frac{3}{3}}$ as ${({(x + 8)}^{\frac{1}{3}})}^{3}$ .

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

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = 1$ and $b = {(x + 8)}^{\frac{1}{3}}$ .

${(x + 8)}^{\frac{1}{3}} ((1 - {(x + 8)}^{\frac{1}{3}}) (1^{2} + 1 {(x + 8)}^{\frac{1}{3}} + {({(x + 8)}^{\frac{1}{3}})}^{2}))$

Factor.

Simplify.

One to any power is one.

${(x + 8)}^{\frac{1}{3}} ((1 - {(x + 8)}^{\frac{1}{3}}) (1 + 1 {(x + 8)}^{\frac{1}{3}} + {({(x + 8)}^{\frac{1}{3}})}^{2}))$

Multiply ${(x + 8)}^{\frac{1}{3}}$ by $1$ .

${(x + 8)}^{\frac{1}{3}} ((1 - {(x + 8)}^{\frac{1}{3}}) (1 + {(x + 8)}^{\frac{1}{3}} + {({(x + 8)}^{\frac{1}{3}})}^{2}))$

Multiply the exponents in ${({(x + 8)}^{\frac{1}{3}})}^{2}$ .

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

${(x + 8)}^{\frac{1}{3}} ((1 - {(x + 8)}^{\frac{1}{3}}) (1 + {(x + 8)}^{\frac{1}{3}} + {(x + 8)}^{\frac{1}{3} \cdot 2}))$

Combine $\frac{1}{3}$ and $2$ .

${(x + 8)}^{\frac{1}{3}} ((1 - {(x + 8)}^{\frac{1}{3}}) (1 + {(x + 8)}^{\frac{1}{3}} + {(x + 8)}^{\frac{2}{3}}))$

Remove unnecessary parentheses.

${(x + 8)}^{\frac{1}{3}} (1 - {(x + 8)}^{\frac{1}{3}}) (1 + {(x + 8)}^{\frac{1}{3}} + {(x + 8)}^{\frac{2}{3}})$

Factor (x+8)^(1/3)-(x+8)^(4/3)

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