How do you factor #18a ^ { 3} + 52a ^ { 2} b - 6b ^ { 2} a#?

1 Answer
George C.
Jan 13, 2018

#18a^3+52a^2b-6b^2a=2a(9a-b)(a+3b)#

Explanation:

Given:

#18a^3+52a^2b-6b^2a#

Note that all of the terms are divisible by #2a#, so we can separate that out as a factor. In order to complete the square with the remaining quadratic, I will actually separate out a factor #(2a)/9# to avoid fractions in the other expressions...

#18a^3+52a^2b-6b^2a#

#=(2a)/9(81a^2+234ab-27b^2)#

#=(2a)/9((9a)^2+2(9a)(13b)+(13b)^2-196b^2)#

#=(2a)/9((9a+13b)^2-(14b)^2)#

#=(2a)/9((9a+13b)-14b)((9a+13b)+14b)#

#=(2a)/9(9a-b)(9a+27b)#

#=2a(9a-b)(a+3b)#

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