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)#