SOLUTION: Evaluate a^3-b^3 when a-b =2 and a^2+b^2=4.

Question 1055888: Evaluate a^3-b^3 when a-b =2 and a^2+b^2=4.
Answer by ikleyn(52794) (Show Source): You can put this solution on YOUR website!
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Evaluate a^3-b^3 when a-b =2 and a^2+b^2=4.
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Take a-b = 2 and square both sides.

You will get

a^2 - 2ab + b^2 = 4.

Replace here (a^2 + b^2) by 4 (according to the condition).

You will get

4 - 2ab = 4.

It implies ab = 0.

Now a^3 - b^3 = (a-b)*(a^2 +ab + b^2) (standard decomposition/factoring).

Now replace here a-b by 2; replace a^2+b^2 by 4 and replace ab by 0.

You will get

a^3 - b^3 = 2*(4 + 0) = 8.

Answer.  Then  a^3 - b^3 = 8.

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