Question:
If $a-b=6$ and $a b=20$, find the value of $a^{3}-b^{3}$
Solution:
Given,
a – b = 6 and ab = 20
We know that,
$a^{3}-b^{3}=(a-b)^{3}+3 a b(a-b)$
$\Rightarrow a^{3}-b^{3}=(a-b)^{3}+3 a b(a-b)$
$\Rightarrow a^{3}-b^{3}=(6)^{3}+3(20)(6)$
$\Rightarrow a^{3}-b^{3}=216+360$
$\Rightarrow a^{3}-b^{3}=576$
Hence, the value of $a^{3}-b^{3}$ is 576
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