Find the value of $(47)^{3}$ using the short-cut or column method

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Solution

$47^{3} = {(50 - 3)}^{3}$
It is the form of ${(a - b)}^{3}$ , where $a = 50, b = 3$
Applying the formula ${(a - b)}^{3} = a^{3} - b^{3} - 3 a b (a - b)$
$47^{3} = {(50 - 3)}^{3} = 50^{3} - 3^{3} - 3 \times 50 \times 3 \times (50 - 3) = 125000 - 27 - 21150 = 103823$

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Find the value of each of the following using the short-cut method:
1. $(25)^{3}$ 2. $(47)^{3}$ 3. $(68)^{3}$ 4. $(84)^{3}$

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