Question

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

Answer 1

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

Explanation:

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