How do you factor #8u^3+27#?

1 Answer
Jan 5, 2016

Answer:

#8u^3+27=(2u+3)(4u^2-6u+9)#

Explanation:

#8u^3+27#

Since #8u^3# and #27# are cubes, we can rewrite the expression as #(2u)^3+(3)^3#.

This a sum of two cubes with the form #a^3+b^3=(a+b)(a^2-ab+b^2)#, where #a=2u# and #b=3#.

Substitute the values for #a# and #b# into the equation.

#(2u)^3+(3)^3=(2u+3)(2u)^2-(2u)(3)+(3)^2#

Simplify.

#(2u)^3+(3)^3=(2u+3)(4u^2-6u+9)#