How do you multiply (2x+2y)/(x+y) *( x^2-y^2)/(2x-2y)2x+2yx+yx2y22x2y?

1 Answer
Mar 26, 2018

x+yx+y

Explanation:

(2x+2y)/(x+y)*(x^2-y^2)/(2x-2y)2x+2yx+yx2y22x2y

Factoring:

(2(x+y))/(x+y)*(x^2-y^2)/(2(x-y))2(x+y)x+yx2y22(xy)

Cancelling:

(cancel(2)(x+y))/(x+y)*(x^2-y^2)/(cancel(2)(x-y))

(x+y)/(x+y)*(x^2-y^2)/(x-y)

Further factoring:

(x+y)/(x+y)*((x+y)(x-y))/(x-y)

Cancelling again:

cancel((x+y))/cancel((x+y))*((x+y)cancel((x-y)))/cancel((x-y))

1*(x+y)=x+y