SOLUTION: factor x2+4xy+4y2-16 factor 12(x+1)2-17(x+1)+6

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Question 39793: factor x2+4xy+4y2-16
factor 12(x+1)2-17(x+1)+6

Found 2 solutions by stanbon, AnlytcPhil:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
factor x2+4xy+4y^2-16
= (x+2y)^2-4^2
=(x+2y-4)(x+2y+4)
factor 12(x+1)^2-17(x+1)+6
=[(4(x+1)-3)][(3(x+1)-2]
=[4x+1][3x+1]
Cheers,
Stan H.

Answer by AnlytcPhil(1808) About Me  (Show Source):
You can put this solution on YOUR website!
Factor            x² + 4xy + 4y² - 16



We have to recognize that the first three terms

will factor as a perfect square:



                  x² + 4xy + 4y² - 16



                (x + 2y)(x + 2y) - 16



                       (x + 2y)² - 16



Now this factors again as the difference of two squares



                       (x + 2y)² - 4²



               [(x + 2y) - 4][(x + 2y) + 4]



                 [x + 2y - 4][x + 2y + 4]



                 (x + 2y - 4)(x + 2y + 4)









factor         12(x + 1)² - 17(x + 1) + 6 



Replace (x + 1) by a single letter, say W, then

W = (x + 1)



                   12W² - 17W + 6



                  (3W - 2)(4W - 3)



Change the parentheses to brackets, then replace the

W's with (x + 1)



              [3(x + 1) - 2][4(x + 1) - 3]



                [3x + 3 - 2]{4x + 4 - 3]



                    (3x + 1)(4x + 1)   



Edwin

AnlytcPhil@aol.com