Asked by Lily
How would you factor
(x+y)^2-(x-y)^2
(x+y)^2-(x-y)^2
Answers
Answered by
Reiny
recall the difference of squares:
a^2 - b^2 = (a+b)(a-b)
this has the same pattern
(x+y)^2-(x-y)^2
= (x+y + x-y)(x+y - (x-y))
= 2x(2y)
= 4xy
or you could just expand the original ...
(x+y)^2-(x-y)^2
= x^2 + 2xy + y^2 - (x^2 - 2xy + y^2)
= 4xy
a^2 - b^2 = (a+b)(a-b)
this has the same pattern
(x+y)^2-(x-y)^2
= (x+y + x-y)(x+y - (x-y))
= 2x(2y)
= 4xy
or you could just expand the original ...
(x+y)^2-(x-y)^2
= x^2 + 2xy + y^2 - (x^2 - 2xy + y^2)
= 4xy
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