# How do you factor #27x^3 - 27y^3#?

##### 2 Answers

#### Explanation:

This is the difference of cubes and has a set pattern.

make 2 brackets:

The first is simply the cube root of each term

The second bracket is formed from the first in 5 steps:

#### Explanation:

The first step here is to take out a

#color(blue)"common factor"# of 27.

#rArr27(x^3-y^3)........ (A)# Now

#x^3-y^3# is a#color(blue)"difference of cubes"# and in general factorises as.

#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)|)))# here a = x and b = y

Substituting this result into (A) gives the factorised form.

#rArr27x^3-27y^3=27(x-y)(x^2+xy+y^2)#