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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