How do you simplify #(x + y)(x - y)#?

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Answer 1 · 2016-07-22T05:04:14

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

To simplify #(x+y)(x-y)# we use distributive property of number systems.

Let us treat #(x+y)# as a single number and distribute it over #(x-y)#.

This makes #(x+y)(x-y)#

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

Now using commutative property of multiplication the above is equivalent to

#x(x+y)-y(x+y)# and now again using distributive property this is equivalent to

#x xx x+x xx y- y xx x-yxxy#

#x xx x+x xx y- x xx y-yxxy#

= #x^2+xy-xy-y^2#

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

= #x^2-y^2#