How do you factor completely $ax^2-9a+bx^2-9b$ ?

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Answer 1 · 2015-11-13T20:24:14

$(a+b)(x-3)(x+3)$

Look for 'repeats' and 'play' to see if they can be used to your advantage!

Write as:

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

Then we have

$(a+b)(x^2-9)$ .............................. (1)

Not finished yet! Remember that $(c^2-d^2)=(c-d)(c+d)$

I have just spotted that we have this situation in the previous line of the solution. $9 -> 3^2$

Rewrite (1) as:

$(a+b)(x^2-3^2)$ .............................. (3)

Expanding (3) gives:

$(a+b)(x-3)(x+3)$

How do you factor completely ax^2-9a+bx^2-9bax^2-9a+bx^2-9b?