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

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

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Answer 1 · 2018-03-21T11:24:58

In factored form this is:

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

Explanation:

The difference of squares identity can be written:

$A^{2} - B^{2} = (A - B) (A + B)$ $A^2-B^2 = (A-B)(A+B)$

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

Given:

$x^{2} + 2 a x = b^{2} - a^{2}$ $x^2+2ax = b^2-a^2$

Add $a^{2} - b^{2}$ $a^2-b^2$ to both sides to get:

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

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

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

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

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

1 Answer

Explanation:

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How do you factor completely x^2+2ax = b^2-a^2x2+2ax=b2−a2x^2+2ax = b^2-a^2?

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Explanation:

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