SOLUTION: Please help with the following: Factor: 64𝑚^4 − 27𝑚𝑛^3 Thank you!

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Question 1094764: Please help with the following:
Factor: 64𝑚^4 − 27𝑚𝑛^3
Thank you!
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
= m%2A%2864m%5E3+-+27n%5E3%29 = m%2A%28%284m%29%5E3-%283n%29%5E3%29 = m%2A%284m+-+3n%29%2A%28%284m%29%5E2+%2B+%284m%29%2A%283n%29+%2B+%283n%29%5E2%29,

and you may simplify it further, if you want.


The basic identity is  a%5E3+-+b%5E3%29 = %28a-b%29%2A%28a%5E2+%2B+ab+%2B+b%5E2%29,


which you must memorize.


1. The cube of the sum formula is                 %28a+%2B+b%29%5E3+=+a%5E3+%2B+3a%5E2%2Ab+%2B+3a%2Ab%5E2+%2B+b%5E3.
      For details and examples of applications of this formula see the lesson The cube of the sum formula in this site.


2. The cube of the difference formula is     %28a+-+b%29%5E3+=+a%5E3+-+3a%5E2%2Ab+%2B+3a%2Ab%5E2+-+b%5E3.
      For details and examples of applications of this formula see the lesson The cube of the difference formula in this site.


3. The sum of cubes formula is                       a%5E3+%2B+b%5E3+=+%28a+%2B+b%29%2A%28a%5E2+-+ab+%2B+b%5E2%29.
      For details and examples of applications of this formula see the lesson The sum of cubes formula in this site.

4. The difference of cubes formula is           a%5E3+-+b%5E3+=+%28a+-+b%29%2A%28a%5E2+%2B+ab+%2B+b%5E2%29.
      For details and examples of applications of this formula see the lesson The difference of cubes formula in this site.