Evaluate $95^{3}$

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Solution

Given expression can be written as
${(95)}^{3} = {(100 - 5)}^{3}$
We know that
${(a - b)}^{3} = a^{3} - b^{3} - 3 a b (a - b)$
$\begin{array}{rcl} \Rightarrow & {(100 - 5)}^{3} = {(100)}^{3} - {(5)}^{3} - 3 \times 100 \times 5 (100 - 5) \end{array}$
$\begin{array}{rcl} = & 1000000 - 125 - 1500 (95) \\ = & 1000000 - 125 - 142500 \\ = & 8, 57, 375 \end{array}$
Hence, $95^{3} = 8, 57, 357$ .

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(95)^{3}

Write the integers in decreasing order :- $- 167, - 237, - 953, 1$ .

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