SOLUTION: factorize 64 - (b-2)^3

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Question 167733: factorize
64 - (b-2)^3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let z=b-2

So the expression 64+-+%28b-2%29%5E3 then becomes 64-z%5E3


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64-z%5E3 Start with the given expression.


%284%29%5E3-%28z%29%5E3 Rewrite 64 as %284%29%5E3. Rewrite z%5E3 as %28z%29%5E3.


%284-z%29%28%284%29%5E2%2B%284%29%28z%29%2B%28z%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


Note: in this case, A=4 and B=z



%284-z%29%2816%2B4z%2Bz%5E2%29 Multiply


%284-%28b-2%29%29%2816%2B4%28b-2%29%2B%28b-2%29%5E2%29 Plug in z=b-2


%284-%28b-2%29%29%2816%2B4%28b-2%29%2Bb%5E2-4b%2B4%29 FOIL


%284-b%2B2%29%2816%2B4b-8%2Bb%5E2-4b%2B4%29 Distribute


%28-b%2B6%29%28b%5E2%2B12%29 Combine like terms.


-%28b-6%29%28b%5E2%2B12%29 Factor a negative 1 from -b%2B6 to get -%28b-6%29



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Answer:


So 64+-+%28b-2%29%5E3 factors to -%28b-6%29%28b%5E2%2B12%29