What is the value of $a^{3} - b^{3}$ ?

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Solution

$(a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)$
$a^{3} - b^{3} = (a - b)^{3} + 3 a b (a - b)$
$a^{3} - b^{3} = (a - b) [(a - b)^{2} + 3 a b]$
$a^{3} - b^{3} = (a - b) (a^{2} - 2 a b + b^{2} + 3 a b)$
$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$

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If the value of $(\frac{a^{3} - b^{3}}{a^{3} + b^{3}})$ when a = 7 and b = 2 is $\frac{335}{p}$ , then p is 321.

If the value of $(\frac{a^{3} - b^{3}}{a^{3} + b^{3}})$ , when $a = 7$ and $b = 2$ is $\frac{335}{p}$ , then $p$ is $321$ .

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