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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Updated on: 10-Oct-2022

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