Question

Simplify completely

Answer 1

I have a ridiculous amount of homework tonight and I've worked forever on this problem and still can't get it right. Can someone please help?

Answer 2

first step would be to factor out all common terms:

\[\frac{ 4(x^2 - 4) }{ 2(x^2 + 4x + 4) }*\frac{ 4x^2(x^2 + 2x + 4) }{ 8x^4(x^3 - 8) }\]

apply difference of squares "shortcut" and also diff of cubes shortcut which is:
\[a^3 - b^3 = (a-b)(a^2 + ab + b^2)\]
re-arranges to:\[\frac{ 2(x+2)(x-2) }{ (x+2)(x+2) }* \frac{ x^2 + 2x + 4 }{ 2x^2 (x-2)(x^2 + 2x + 4) } = \frac{ 2(x-2) }{ (x+2) }*\frac{ 1 }{ 2x^2(x-2) } = \frac{ 1 }{ x^2(x+2) }\]

Answer 3

The a^3-b^3 was probably where I got lost. Thank you so much. You are a life saver :)

Answer 4

glad i could help ^_^