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

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Answer 1 · 2016-01-05T04:21:13

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

#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)#