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If $a – b = 6$ and $ab = 20$, find the value of $a^3-b^3$.
Given:
$a – b = 6$ and $ab = 20$
To do:
We have to find the value of $a^3 - b^3$.
Solution:
We know that,
$(a + b)^3 = a^3 + b^3 + 3ab(a + b)$
Therefore,
$a - b = 6$
Cubing both sides, we get,
$(a - b)^3 = (6)^3$
$a^3 - b^3 - 3ab(a - b) = 216$
$a^3 - b^3 - 3 \times 20 \times 6 = 216$
$a^3 - b^3 - 360 = 216$
$a^3 -b^3 = 216 + 360 = 576$
Hence, $a^3 - b^3 = 576$. 
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