$4^{3}$ - $3^{3}$ = ___ + 3 $\times$ 4 $\times$ 3.

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Solution

$4^{3}$ - $3^{3}$ = a + 4 $\times$ 3 $\times$ 3
This one is based on the following identities.
$(a - b)^{3}$ = $a^{3}$ - $b^{3}$ - 3ab (a - b)
$(4 - 3)^{3}$ = $4^{3}$ - $3^{3}$ - 3 $\times$ 4 $\times$ 3
1 = $4^{3}$ - $3^{3}$ - 3 $\times$ 4 $\times$ 3
$4^{3}$ - $3^{3}$ = 1 + 3 $\times$ 4 $\times$ 3
a = 1

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