How do you factor #8a^3-27#?

1 Answer
Feb 2, 2016

Answer:

#(2x-3)(2x^2+6x+9)#

Explanation:

1) Decide factoring method

In the equation both #8# and #27# are cubes so we can use the Difference of Cubes method of factoring

2) Solve for variables

The formula for the Difference of Cubes method is:
#a^3-b^3=(a-b)(a^2+ab+b^2)#

First we find #a#:
#a^3=8a^3#
#root(3)(a^3)=root(3)(8a^3)#
#a=2a#

Then we find #b#:
#b^3=27#
#root(3)(b^3)=root(3)(27)#
#b=3#

3) Fill in formula

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

#(2x)^3-3^3=(2x-3)(2x^2+(2x*3)+3^2)#

4) Simplify

#(2x-3)(2x^2+6x+9)#