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If $a - b = 4$ and $ab = 21$, find the value of $a^3-b^3$.
Given:
$a - b = 4$ and $ab = 21$
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,
$a - b = 4$
Cubing both sides, we get,
$(a - b)^3 = (4)^3$
$a^3 - b^3 - 3ab (a - b) = 64$
$a^3 - b^3 - 3 \times 21 \times 4 = 64$
$a^3 - b^3 - 252 = 64$
$a^3 - b^3 = 64 + 252$
$a^3 - b^3 = 316$
Hence, the value of $a^3 - b^3$ is 316.
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