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

Question

2792 views around the world

You can reuse this answer
Creative Commons License

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.

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

How do you factor 8u^3+278u^3+27?