How do you factor # m² + 2mn + n² - x² + 2xy - y²#?

1 Answer
Apr 22, 2016

#(m+n)^2 - (x-y)^2#

Explanation:

#m^2+2mn+n^2 - x^2 +2xy-y^2#

Group the elements so that the #m,n# elements are together and the #x,y# elements are together. Bracketing the #x,y# elements together with a minus sign before them means changing the signs for the #2xy# and #y^2# elements.

#=(m^2+2mn+n^2)-(x^2-2xy+y^2)#

Each of these expressions can now be individually factored as the sum of squares (#m,n#) and the difference of squares (#x,y#)

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