How do you factor 3a^2+8ab-3b^2?

1 Answer
George C.
Apr 21, 2016

Use an AC method to find:

3a^2+8ab-3b^2=(3a-b)(a+3b)

Explanation:

Note that this is a homogeneous polynomial: All of the terms are of degree 2. So we can factor using a similar technique to that which we would use for a quadratic in one variable.

Use an AC Method:

Find a pair of factors of AC = 3*3 = 9 which differ by 8.

The pair 9, 1 works.

Use that pair to split the middle term and factor by grouping:

3a^2+8ab-3b^2

=3a^2+9ab-ab-3b^2

=(3a^2+9ab)-(ab+3b^2)

=3a(a+3b)-b(a+3b)

=(3a-b)(a+3b)

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