Simplify the following expression.
$\frac{(62×62×62)-3(62×62×22)+3(62×22×22)-(22×22×22)}{8×8×8}$
Answer & explanation
Correct answer: option 3
$\frac{(62×62×62)-3(62×62×22)+3(62×22×22)-(22×22×22)}{8×8×8}$
(a - b)3 = a3 - b3 - 3ab(a-b)
Here a = 62 and b = 22
So,
$\frac{(62×62×62)-3(62×62×22)+3(62×22×22)-(22×22×22)}{8×8×8}$ = \(\frac{(62-22)^3}{512}\)
= \(\frac{64000}{512}\) = 125