Question #71d2a

2 Answers
Jun 17, 2017

See a solution process below:

Explanation:

First, rewrite the third term as:

x^2(a - b) - 6x(a - b) - 9(-1(a - b)) =>

x^2(a - b) - 6x(a - b) + 9(a - b)

We can now factor and (a - b) out of each term giving:

(a - b)(x^2 - 6x + 9)

We can now factor the quadratic as:

(a - b)(x - 3)(x - 3)

Or

(a - b)(x - 3)^2

Jun 17, 2017

x^2(a-b)-6x(a-b)-9(b-a) can be written as

x^2(a-b)-6x(a-b)-(-9)(a-b), taking -1 common from the last bracket.
=x^2(a-b)-6x(a-b)+9(a+b)

Taking (a-b) common from the whole expression we get

(a-b)(x^2 -6x+9)

(x^2 -6x+9) is simply (x-3)^2

So, the expression can be factorised as

x^2(a-b)-6x(a-b)-9(b-a)=(a-b)(x-3)^2

Hope this helps.

Feel free to comment if you want further explanation of any step.