# If a - b = 4 and ab = 21, Find the value of a3 - b3

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 $a^{3}-b^{3}=316$
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