Question

Factor and simplify the algebraic expression.
(x+7)^1/4 - (x+7)^5/4

Answer 1

\[(x+7)^{\frac{1}{4}}-(x+7)^{\frac{5}{4}}\]
\[=(x+7)^{\frac{1}{4}}(1-(x+7)^{\frac{4}{4}})\] is a start

Answer 2

Isn't (x+7)^1/4 the GCF?

Answer 3

then then next step, since \(\frac{4}{4}=1\) is to rewrite as
\[=(x+7)^{\frac{1}{4}}(1-(x+7))\]

Answer 4

it is the GCF and that is why you factor it out

Answer 5

so my original equation = what you just gave me?

Answer 6

the "final answer" would be
\[(x+7)^{\frac{1}{4}}(-x-6)\] or
\[-(x+6)(x+7)^{\frac{1}{4}}\] sicnce \(1-(x+7)=-x-6\)

Answer 7

But I thought that (1-(x+7)) = -x-7 because you distribute the negative and then the one makes it stay the same... right?