# How do you factor #27k^3+64d^3#?

##### 2 Answers

Aug 29, 2016

#### Explanation:

The sum of cubes identity can be written:

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

We can use this with

#27k^3+64d^3#

#=(3k)^3+(4d)^3#

#=(3k+4d)((3k)^2-(3k)(4d)+(4d)^2)#

#=(3k+4d)(9k^2-12kd+16d^2)#

That is as far as we can go with Real coefficients. If we allow Complex coefficients then this can be factored further as:

#=(3k+4d)(3k+4omegad)(3k+4omega^2d)#

where

Aug 29, 2016

=

#### Explanation:

This difficulty is recognising that the values are all cubes.

This expression is the sum of cubes.