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

Nov 13, 2015

$\left(a + b\right) \left(x - 3\right) \left(x + 3\right)$

Explanation:

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

Write as:

${x}^{2} \left(a + b\right) - 9 \left(a + b\right)$

Then we have

$\left(a + b\right) \left({x}^{2} - 9\right)$.............................. (1)

Not finished yet! Remember that$\left({c}^{2} - {d}^{2}\right) = \left(c - d\right) \left(c + d\right)$

I have just spotted that we have this situation in the previous line of the solution. $9 \to {3}^{2}$

Rewrite (1) as:

$\left(a + b\right) \left({x}^{2} - {3}^{2}\right)$.............................. (3)

Expanding (3) gives:

$\left(a + b\right) \left(x - 3\right) \left(x + 3\right)$