Question

(PLESE HELP) Factor the following expression. Simplify your answer.

5p(p + 2)^-2/3 +4(p +2)^1/3

plese explain your answer

Answer 1

The factor of the expression $5p(p + 2)^{\frac{2}{3} } + 4(p + 2)^{\frac{1}{3} }$ is$(p + 2)^{\frac{2}{3} } (5p^{3} + 10p^{2} + 20p + 4)$

To answer the question, we need to know what factorization is

What is factorization?

Factorization is the process of breaking down an expressing into a simpler form containing its factors.

Since

$5p(p + 2)^{\frac{2}{3} } + 4(p + 2)^{\frac{1}{3} }$

Since $(p + 2)^{\frac{1}{3} }$ is common, we factor it out. So, we have

$(p + 2)^{\frac{2}{3} } (5p(p + 2)^{2} + 4)$

Expanding the bracket, we have

$(p + 2)^{\frac{2}{3} } (5p(p^{2} + 2p + 4) + 4) = (p + 2)^{\frac{2}{3} } (5p^{3} + 10p^{2} + 20p + 4)$

So, the factor of the expression $5p(p + 2)^{\frac{2}{3} } + 4(p + 2)^{\frac{1}{3} }$ is$(p + 2)^{\frac{2}{3} } (5p^{3} + 10p^{2} + 20p + 4)$

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