How do you simplify (x^2-xy+y^2)(x-y)?

Answer 1

(x^2 - xy + y^2) (x - y)
It seems to me that this is already fairly simple, but you could
distribute (multiply the trinomial & binomial together.)
x^3 - yx^2 + xy^2 - yx^2 + xy^2 - y^3
now, combine like terms
x^3 -2yx^2 + 2xy^2 - y^3

Answer 2

First: Multiply all components in (x^2-xy+y^2) with the x in the second equation. This yields: x^3-(x^2)y+x(y^2)
Secondly: Repeat this operation, but this time multiply everything in the first equation with the y of the second equation, which should result in: -y(x^2)+x(y^2)-y^3

Thirdly: Now place step one and two together:
=> x^3-(x^2)y-x^2+x(y^2)+x(y^2)-y^3


Simplify (Subtract and add alikes): x^3-2x^2+2x(y^2)-y^3

Answer 3

You multiply it out.
First, multiply each of the 3 terms in the first factor by the first term of the second factor:
x^2 times x, then -xy times x, then +y^2 times x
Write down these 3 results.

Then multiply each of the 3 terms in the first factor by the second term of the second factor:
x^2 times -y, then -xy times -y, then +y^2 times -y
Write down these 3 results.

Then take the 6 results that you wrote down and combine them.
Any two terms that are similar can be combined. For example, if you had 5xy and -3xy, you could combine them to get 2xy.

That's all you need to do.
Hint: The preceding response had the right idea, but he messed up and gave you the wrong answer. Don't use his answer.

Good luck.

Answer 4

take the (x^2-xy+y^2) and first multiply it by the x in (x-y), so you get
(x^3-x^2y+xy^2)
meanwhile, multiply the (x^2-xy+y^2)by the y, so you get(x^2 y-xy^2+y^3). now subtract the first from the second (since the orignal equation has (x-y) and you get:
(x^3-x^2y+xy^2)-(x^2 y-xy^2+y^3).
x^3-x^2y+xy^2-x^2+xy^2+y^3.
combine like terms:
x^3-x^2y+2xy^2-x^2+y^3. to simplify further, factor
x(x^2-xy+2y^2-x+y^3)

Answer 5

Woah, I should put my homework here so others can do it for me. ;)

Answer 6

DYOH!