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

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Answer 1 · 2018-03-26T12:30:49

#x+y#

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

Factoring:

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

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#