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