need help with basic algebra problem

**cornman** · February 19th 2009, 08:55 PM

the problem is:

(x^2 - y^2)^2 / x^2 + 2xy + y2

the answer is supposed to be:

x^2 - 2xy +y2

i get to x^2 - 2x^2y^2 + y^2 / 2xy

what am i missing?

thanks

**mollymcf2009** · February 19th 2009, 09:07 PM

Originally Posted by cornman

the problem is:

(x^2 - y^2)^2 / x^2 + 2xy + y2

the answer is supposed to be:

x^2 - 2xy +y2

i get to x^2 - 2x^2y^2 + y^2 / 2xy

what am i missing?

thanks

You need to split your numerator into $(x^2-y^2)(x^2-y^2)$ and FOIL it to get $x^4 - 2x^2y^2 + y^4$ then cancel.

**ADARSH** · February 19th 2009, 09:10 PM

Originally Posted by cornman

the problem is:

(x^2 - y^2)^2 / x^2 + 2xy + y2

the answer is supposed to be:

x^2 - 2xy +y2

i get to x^2 - 2x^2y^2 + y^2 / 2xy

what am i missing?

thanks

$ {(x^2-y^2) =(x+y)(x-y)} $

$ {(x+y)^2 = (x^2 +2xy +y^2) } $

$ {(x-y)^2 = (x^2-2xy +y^2)} $

$ (x^2-y^2)^2 =(x+y)^2(x-y)^2...........\text{Use in numerator} $

$ (x^2 +2xy +y^2)= (x+y)^2 ...........\text{Use in denominator} $

$ (x^2-2xy +y^2)=(x-y)^2 ...........\text{use in the last step} $

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