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!

Thanks for your help, guys.

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

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)

$\displaystyle x(2x-y)-x(x-y)-y(x+2y)=2x^2-xy-x^2+xy-xy-2y^2$

Re: Simplification with Brackets

Quote:

Originally Posted by

**Plato** $\displaystyle x(2x-y)-x(x-y)-y(x+2y)=2x^2-xy-x^2+xy-xy-**2y^2**$

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?

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.

$\displaystyle -y(x+2y)=-xy-2y^2$.