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