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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.
