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Simplify:$ \frac{155 \times 155 \times 155-55 \times 55 \times 55}{155 \times 155+155 \times 55+55 \times 55} $
Given:
\( \frac{155 \times 155 \times 155-55 \times 55 \times 55}{155 \times 155+155 \times 55+55 \times 55} \)
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,
$\frac{155 \times 155 \times 155-55 \times 55 \times 55}{155 \times 155+155 \times 55+55 \times 55}$
Let $a=155$ and $b=55$
This implies,
$\frac{155 \times 155 \times 155-55 \times 55 \times 55}{155 \times 155+155 \times 55+55 \times 55}=\frac{a^{3}-b^{3}}{a^{2}+a b+b^{2}}$
$=\frac{(a-b)(a^{2}+a b+b^{2})}{a^{2}+a b+b^{2}}$
$=a-b$
$=155-55$
$=100$
Hence, $\frac{155 \times 155 \times 155-55 \times 55 \times 55}{155 \times 155+155 \times 55+55 \times 55}=100$.
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