Question 39793
<pre><font size = 4><b>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