Question

Simplify: $\frac{[155\times 155\times 155-55\times 55\times 55]}{[155\times 155+155\times 55+55\times 55]}$

Answer 1

simplify the expression :

The given expression is $\frac{[155\times 155\times 155-55\times 55\times 55]}{[155\times 155+155\times 55+55\times 55]}$

$\begin{array}{rcl}& & \\ \frac{[155\times 155\times 155-55\times 55\times 55]}{[155\times 155+155\times 55+55\times 55]}& =& \frac{{\left(155\right)}^3-{\left(55\right)}^3}{{\left(155\right)}^3\times 155+(155\times 55)+{\left(55\right)}^2}\\ & =& \frac{(155-55)\left[(155{)}^2+(155\times 55)+(55{)}^2\right]}{(155{)}^2+(155\times 55)+(55{)}^2}\left[\because x^3-y^3=(x-y)\left(x^2+y^2+xy\right)\right]\\ & =& 155-55\\ & =& 100\end{array}$

Therefore, value of the given expression is $\frac{[155\times 155\times 155-55\times 55\times 55]}{[155\times 155+155\times 55+55\times 55]}=100$