How do you factor #(3x-4)^3 + 27#?

1 Answer
Jim H
Apr 10, 2015

This is a sum of two cubes. Memorize the rule:

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

In this example, #a=color(red)((3x-4))# and #b=3#, so

#color(red)((3x-4)^3)+3^3=(color(red)((3x-4))+3)(color(red)((3x-4)^2)-color(red)((3x-4))3+3^2)#

This answer can be simplified to get:

#(3x-1)(x^2-24x+16-9x+12+9)=(3x-1)(x^2-33x+37)#

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