Simplify:$ \frac{173 \times 173 \times 173+127 \times 127 \times 127}{173 \times 173-173 \times 127+127 \times 127} $

Given:

\( \frac{173 \times 173 \times 173+127 \times 127 \times 127}{173 \times 173-173 \times 127+127 \times 127} \)

To do:

We have to simplify the given expression.

Solution:

We know that,

$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$

$a^3 - b^3 = (a - b) (a^2 + ab + b^2)$

Therefore,

$\frac{173 \times 173 \times 173+127 \times 127 \times 127}{173 \times 173-173 \times 127+127 \times 127}$

Let $a=173$ and $b=127$

This implies,

$\frac{173 \times 173 \times 173+127 \times 127 \times 127}{173 \times 173-173 \times 127+127 \times 127} = \frac{a^{3}+b^{3}}{a^{2}-a b+b^{2}}$

$=\frac{(a+b)(a^{2}-a b+b^{2})}{a^{2}-a b+b^{2}}$

$=a+b$

$=173+127$

$=300$

Hence, $\frac{173 \times 173 \times 173+127 \times 127 \times 127}{173 \times 173-173 \times 127+127 \times 127} = 300$.

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Updated on: 10-Oct-2022

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