How do you factor #m^3 + 64n^3#?

1 Answer
Mar 14, 2018


#m^3 +64n^3 = (m+4n)(m^2-4mn +16n^2)#


This type of expression is known as the 'sum of two cubes', because both of the terms are perfect cubes.

Note the form of the factoring:

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

Following the method shown we will have:

#m^3 +64n^3 = (m+4n)(m^2-4mn +16n^2)#

To factor the sum or difference of two cubes:

This is how it is done:

Make Two brackets,
The first is found from the cube root of each term.
The second bracket is formed from the first to get three terms:

  • square the first term
  • change the sign
  • multiply the two terms together
  • PLUS
  • square the second term