Factor. x(2y - x )² + 2x²( x - 2y ) =?

Question

EVIL, I Can tell you, EVil, they are the axis of EviL of Death!

I can pretty much do almost the whole homework packet but Im ALWAYS stuck on ²

FACTOR.
Given:


I cant do it, its tooo hard! Impossible!
Please give steps, Im 15, factor please.

Answer 1

(2y - x )² = (x-2y)²

So x(2y - x )² + 2x²(x - 2y)

= x(x-2y)² + 2x²( x - 2y )

= x(x-2y)[(x-2y) + 2x]

= x(x-2y)(3x-2y)

please check for mistakes.
but this is the key idea: (2y-x)²=(x-2y)².

Answer 2

Note: Unfortunately, I could not find a way to superscript the powers. My apologies for any possible misinterpretations of the following text.

Tiger: Ya, I know how you feel. Algebra can be exasperating, but don’t let it get you down. If this confusion persists, I suggest you get a professional tutor. Working one on one with a consultant is the way to go.

Anyway, it’s been a while since I’ve had to do this stuff, but I’m 99.9% sure the following solution is correct.

1.) x(2y – x)2 + 2x2(x – 2y)

2.) x(2y2 – x2) + 2x3 – 4x2y

3.) 2xy2 – x3 + 2x3 – 4x2y = Solution

First, you must work with what is in parentheses. EVERYTHING in parentheses becomes subject to any subsequent power(s). Then you can multiply what is in parentheses by any preceding variable(s). When multiplying powers, the result is addition. For example, x2 multiplied by x3 would become x5, or x multiplied by x would become x2.

Answer 3

All you really need to do is to use a -1 to reverse one of the parentheticals:

x(2y - x)^2 + 2x^2(x - 2y)
= x(2y - x)^2 - 2x^2 (2y - x)
= (2y-x)(x(2y-x) - 2x^2)
= (2y-x)(2xy-x^2 - 2x^2)
= (2y-x)(2xy - 3x^2)
= x(2y - x)(2y - 3x)

Hope that helps.

Answer 4

2x².(x - 2y) + x.[(-1)(x - 2y)]²
2x².(x - 2y) + x.(x - 2y)²
x.(x - 2y).(2x + (x - 2y))
x.(x - 2y).(3x - 2y)