SOLUTION: Please simplify: (x+y)(x^2+2xy-y)^2

Question 251796: Please simplify:
(x+y)(x^2+2xy-y)^2

Found 2 solutions by jim_thompson5910, richwmiller:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, let's expand

Start with the given expression.

Rewrite as

Expand. Recall that

Distribute.

Multiply.

Now combine like terms.

So expands to .

In other words, .

------------------------------------------------------------------------------

This means that then becomes

Now let's finish up...

Start with the given expression.

Expand.

Distribute.

Multiply.

Now combine like terms.

So expands to .

In other words, .

==========================================================================

Answer:

So fully expands out to

In other words,

Note: if this problem was more complicated than it should have been, then maybe there's a typo somewhere.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Believe me this can't be simplified.
It can be expanded and multiplied out.
(x^(2)+2xy-y)^2 becomes x^4+4 x^3 y+4 x^2 y^2-2 x^2 y-4 x y^2+y^2
and then you still have to multiply by (x+y)
and that can become
x^5+(5 x-2) x^3 y+(8 x^2-6 x+1) x y^2+(2 x-1)^2 y^3
or that can become
x^5+5 x^4 y+8 x^3 y^2-2 x^3 y+4 x^2 y^3-6 x^2 y^2-4 x y^3+x y^2+y^3
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