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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Updated on: 10-Oct-2022

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