How do you factor #x^2-4y^2-4x+4# by grouping?
1 Answer
Feb 1, 2017
Explanation:
The difference of squares identity can be written:
#a^2-b^2 = (a-b)(a+b)#
By rearranging the given quadratic, we can recognise it as a difference of squares and hence factor it:
#x^2-4y^2-4x+4 = (x^2-4x+4)-4y^2#
#color(white)(x^2-4y^2-4x+4) = (x-2)^2-(2y)^2#
#color(white)(x^2-4y^2-4x+4) = ((x-2)-2y)((x-2)+2y)#
#color(white)(x^2-4y^2-4x+4) = (x-2y-2)(x+2y-2)#
