SOLUTION: Factor completely: (x+3y)^2-(2x+5y)^2

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Question 74188: Factor completely: (x+3y)^2-(2x+5y)^2
Answer by rmromero(383) About Me  (Show Source):
You can put this solution on YOUR website!


Factor completely: (x+3y)^2-(2x+5y)^2



This is a speacial case: the difference of two squares



           x^2 - y^2 = (x - y) (x + y)







   (x+3y)^2-(2x+5y)^2 = [(x+3y)-(2x+5y)][(x+3y) + (2x+5y)]

                      = [(x+3y)-1(2x+5y)][(x+3y) + (2x+5y)]

                      = (x + 3y - 2x - 5y)(x + 3y + 2x +5y)

                      = (-x - 2y)(3x +8y)