SOLUTION: 2x2(p + q3) - (p + q3) factor completely

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Question 156947: 2x2(p + q3) - (p + q3) factor completely
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2%28p+%2B+q%5E3%29+-+%28p+%2B+q%5E3%29 Start with the given expression


2x%5E2z+-+z Let z=p+%2B+q%5E3 and replace p+%2B+q%5E3 with "z"


z%282x%5E2+-+1%29 Factor out the GCF z


%28p+%2B+q%5E3%29%282x%5E2+-+1%29 Plug in z=p+%2B+q%5E3


So 2x%5E2%28p+%2B+q%5E3%29+-+%28p+%2B+q%5E3%29 factors to %28p+%2B+q%5E3%29%282x%5E2+-+1%29



Note: you can avoid using an extra variable, but it might help simplify things.