I need help with these three questions,
can someone explain to me CLEARLY how to factor each polynomial
1. 125x^6 - 8
2. 64x^12 - 27
3. 8/125x^3 - 64y^6
Hi skeske1234,
Do you know the model for factoring the difference of two cubes?
Review this:
$\displaystyle x^3-y^3=(x-y)(x^2+xy+y^2)$
Apply that to your problems. First let's make them look a bit more like the difference of two cubes.
[1] $\displaystyle (5x^2)^3-(2)^3$
[2] $\displaystyle (4x^4)^3-(3)^3$
[3] $\displaystyle \left(\frac{2}{5}x\right)^3-(4y^2)^3$
I'll do the first one, and you see if that helps you do the other two.
$\displaystyle x^3-y^3=(x-y)(x^2+xy+y^2)$
In my model, let's let $\displaystyle x=5x^2 \ \ and \ \ y=2$
$\displaystyle (5x^2-2)\bigg((5x^2)^2+(2)(5x^2)+(2)^2\bigg)$
$\displaystyle (5x^2-2)(25x^4+10x^2+4$