SOLUTION: simplify/factor (x+2)^3+(x-5)^3

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Question 158096: simplify/factor
(x+2)^3+(x-5)^3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let y=x%2B2 and z=x-5


So %28x%2B2%29%5E3%2B%28x-5%29%5E3 becomes y%5E3%2Bz%5E3


y%5E3%2Bz%5E3 Start with the given expression.


%28y%29%5E3%2B%28z%29%5E3 Rewrite y%5E3 as %28y%29%5E3. Rewrite z%5E3 as %28z%29%5E3.


%28y%2Bz%29%28%28y%29%5E2-%28y%29%28z%29%2B%28z%29%5E2%29 Now factor by using the sum of cubes formula. Remember the sum of cubes formula is A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29


%28y%2Bz%29%28y%5E2-yz%2Bz%5E2%29 Multiply


%28%28x%2B2%29%2B%28x-5%29%29%28%28x%2B2%29%5E2-%28x%2B2%29%28x-5%29%2B%28x-5%29%5E2%29 Plug in y=x%2B2 and z=x-5


%28%28x%2B2%29%2B%28x-5%29%29%28x%5E2%2B4x%2B4-%28x%5E2-3x-10%29%2Bx%5E2-10x%2B25%29 FOIL and expand


%28%28x%2B2%29%2B%28x-5%29%29%28x%5E2%2B4x%2B4-x%5E2%2B3x%2B10%2Bx%5E2-10x%2B25%29 Distribute the negative


%282x-3%29%28x%5E2-3x%2B39%29 Combine like terms.


So %28x%2B2%29%5E3%2B%28x-5%29%5E3 factors to %282x-3%29%28x%5E2-3x%2B39%29


In other words, %28x%2B2%29%5E3%2B%28x-5%29%5E3=%282x-3%29%28x%5E2-3x%2B39%29