# need help with basic algebra problem

• Feb 19th 2009, 08:55 PM
cornman
need help with basic algebra problem
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
• Feb 19th 2009, 09:07 PM
mollymcf2009
Quote:

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 $\displaystyle (x^2-y^2)(x^2-y^2)$ and FOIL it to get $\displaystyle x^4 - 2x^2y^2 + y^4$ then cancel.
• Feb 19th 2009, 09:10 PM
Quote:

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

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

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

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

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

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

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