Question

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

• A. $0$
• B. $100$
• C. $210$
• D. $none$

Answer 1

The correct option is B $100$

We solve the given expression $\frac{155\times 155\times 155-55\times 55\times 55}{155\times 155+155\times 55+55\times 55}$ as shown below:

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

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