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Question:

Simplify the fo llowing expression.

$\frac{(62 \times 62 \times 62) - 3(62 \times 62 \times 22) + 3(62 \times 22 \times 22) - (22 \times 22 \times 22)}{8\times 8\times 8}$​​​​​​​

Explanation:

$\frac{(62 \times 62 \times 62) - 3(62 \times 62 \times 22) + 3(62 \times 22 \times 22) - (22 \times 22 \times 22)}{8\times 8\times 8}$

$\frac{{62}^3-3\times {62}^2\times 22+3\times 62\times {22}^2-{22}^3}{8^3}$

We know, (a - b)³ = a³ - 3a²b + 3ab² - b³

∴ 62³ - 3 × 62² × 22 + 3 × 62 × 22² - 22³ = (62 - 22)³

∴ $\frac{{(62-22)}^3}{8^3}$ = $\frac{{40}^3}{8^3}$ = 53 = 125

Hence, option (c).