Question:
If $a-b=4$ and $a b=21$, Find the value of $a^{3}-b^{3}$
Solution:
Given,
a - b = 4, ab = 21
we know that, $(a-b)^{3}=a^{3}-b^{3}-3 a b(a-b)$..........(1)
substitute a - b = 4 , ab = 21 in eq 1
$\Rightarrow(4)^{3}=a^{3}-b^{3}-3(21)(4)$
$\Rightarrow 64=a^{3}-b^{3}-252$
$\Rightarrow 64+252=a^{3}-b^{3}$
$\Rightarrow 316=a^{3}-b^{3}$
Hence, the value of $a^{3}-b^{3}=316$