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:

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

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

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

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

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