# How do you factor #27m^3+1#?

##### 2 Answers

#### Explanation:

This is a

#color(blue)"sum of cubes"# and is factorised in general as follows.

#color(red)(|bar(ul(color(white)(a/a)color(black)(a^3+b^3=(a+b)(a^2-ab+b^2))color(white)(a/a)|)))#

#27m^3=(3m)^3" and " 1=(1)^3rArra=3m" and " b=1# Substituting these values gives required factors.

#rArr27m^3+1=(3m+1)(9m^2-3m+1)#

Using the formula for the sum of cubes.

#### Explanation:

We can use the formula for the sum of cubes

here our cubes are

The roots of

then are both complex. This means that the quadratic part cannot be factorized more with real numbers. We can write the irreducible factorization in complex numbers as