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)#