Question

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

Answer 1

`(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`