How do you factor completely #x^2+2ax = b^2-a^2#?

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Answer 1 · 2018-03-21T11:24:58

In factored form this is:

#(x+a-b)(x+a+b) = 0#

The difference of squares identity can be written:

#A^2-B^2 = (A-B)(A+B)#

We will use this with #A=(x+a)# and #B=b#.

Given:

#x^2+2ax = b^2-a^2#

Add #a^2-b^2# to both sides to get:

#0 = x^2+2ax+a^2-b^2#

#color(white)(0) = (x+a)^2-b^2#

#color(white)(0) = ((x+a)-b)((x+a)+b)#

#color(white)(0) = (x+a-b)(x+a+b)#