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, $\frac{155 \times 155 \times 155-55 \times 55 \times 55}{155 \times 155+155 \times 55+55 \times 55}=100$.

Tutorialspoint

Updated on: 10-Oct-2022

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