Question #71d2a

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Answer 1 · 2017-06-17T14:24:06

See a solution process below:

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#

Answer 2 · 2017-06-17T14:32:22

#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.