How do you multiply and simplify #(sqrtx + sqrty)(sqrtx - sqrty)#?

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Answer 1 · 2016-11-05T20:49:12

#(sqrtx+sqrty)(sqrtx-sqrty) = **x+y**#

Simplify the expression by multiplying and distributing:
#(sqrtx+sqrty)(sqrtx-sqrty)#
#=x-sqrt(xy)+sqrt(xy)+y#
#=x+y#

Answer 2 · 2016-11-05T20:56:21

See explanation.

There are 2 ways to simplify such expression:

#(sqrt(x)+sqrt(y))xx(sqrt(x)-sqrt(y))=#

#=sqrt(x)*sqrt(x) cancel(-sqrt(x)sqrt(y)) cancel(+sqrt(y)sqrt(x))-sqrt(y)sqrt(y)=sqrt(x^2)-sqrt(y^2)#
#=x-y#

#(x-y)(x+y)=x^2-y^2 # ##

According to the formula we get:

#(sqrt(x)+sqrt(y))(sqrt(x)-sqrt(y))=sqrt(x)^2-sqrt(y)^2=x-y#