math
posted by lomas .
having trouble factoring this particular problem
x^212x+3649y2
factored by grouping
x(x12) (7y6) (7y+6)
the answer in the book has
(x6+7y)(x67y)
confused.

first, notice that the first three terms, x^212x+36, is a perfect square, and can be factored into (x6)(x6),, now rewriting the expression, it becomes:
(x6)^2  49y^2
(x6)^2  (7y)^2
this looks like difference of two squares,, let a = x6 and b=7y, thus:
a^2  b^2
(ab)(a+b)
(x67y)(x6+7y)
so there,, :) 
Gotta remember those damn steps. I immediately assumed it was four terms so I factor by grouping. I forgot that you first look for common factor, then squares etc.
Thanks.