# Simplification with Brackets

#### MathClown

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

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#### Plato

MHF Helper
x=2 y=1 --The following expression is to be simplified: x(2x-y)-x(x-y)-y(x+2y)
$$\displaystyle x(2x-y)-x(x-y)-y(x+2y)=2x^2-xy-x^2+xy-xy-2y^2$$

#### MathClown

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

#### Plato

MHF Helper
How did the x variable get cancelled out??? The final answer is x^2-xy-2y^2 <----
It was never there to begin with.
$$\displaystyle -y(x+2y)=-xy-2y^2$$.