# Simplification with Brackets

• Oct 27th 2012, 04:43 AM
MathClown
Simplification with Brackets
x=2 y=1 --The following expression is to be simplified: x(2x-y)-x(x-y)-y(x+2y)

My book's answer to the above is x^2-xy-2y^2

Can somebody show me, step by step, how that answer was derived. I've been working on it for nearly an hour now and still haven't got it!

EDIT: Specifically, how does the 'x' variable get cancelled out? (The one on the first line.) I don't get why it's 2y^2 and not 2xy^2
• Oct 27th 2012, 05:22 AM
Plato
Re: Simplification with Brackets
Quote:

Originally Posted by MathClown
x=2 y=1 --The following expression is to be simplified: x(2x-y)-x(x-y)-y(x+2y)

$x(2x-y)-x(x-y)-y(x+2y)=2x^2-xy-x^2+xy-xy-2y^2$
• Oct 27th 2012, 05:35 AM
MathClown
Re: Simplification with Brackets
Quote:

Originally Posted by Plato
$x(2x-y)-x(x-y)-y(x+2y)=2x^2-xy-x^2+xy-xy-2y^2$

How did the x variable get cancelled out??? The final answer is x^2-xy-2y^2 <---- how did the x variable get cancelled out?
• Oct 27th 2012, 06:40 AM
Plato
Re: Simplification with Brackets
Quote:

Originally Posted by MathClown
How did the x variable get cancelled out??? The final answer is x^2-xy-2y^2 <----

It was never there to begin with.
$-y(x+2y)=-xy-2y^2$.