SOLUTION: Can you please help me solve this? I'm supposed to factor using the formula {{{(a-b)(a^2-ab+b^2)}}} but I'm not exactly sure how to. {{{27x^3-64}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you please help me solve this? I'm supposed to factor using the formula {{{(a-b)(a^2-ab+b^2)}}} but I'm not exactly sure how to. {{{27x^3-64}}}      Log On


   

Question 189581: Can you please help me solve this? I'm supposed to factor using the formula %28a-b%29%28a%5E2-ab%2Bb%5E2%29 but I'm not exactly sure how to. 27x%5E3-64
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

27x%5E3-64 Start with the given expression.


%283x%29%5E3-%284%29%5E3 Rewrite 27x%5E3 as %283x%29%5E3. Rewrite 64 as %284%29%5E3.


%283x-4%29%28%283x%29%5E2%2B%283x%29%284%29%2B%284%29%5E2%29 Now factor by using the difference of cubes formula. Remember the difference of cubes formula is A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%29


%283x-4%29%289x%5E2%2B12x%2B16%29 Multiply

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Answer:
So 27x%5E3-64 factors to %283x-4%29%289x%5E2%2B12x%2B16%29.


In other words, 27x%5E3-64=%283x-4%29%289x%5E2%2B12x%2B16%29