Question

The value of the expression $\frac{10\times 10\times 10+5\times 5\times 5}{10\times 10-10\times 5+5\times 5}$ is :

• A. 15
• B. 10
• C. 5
• D. 20

Answer 1

The correct option is A 15

$10\times 10\times 10+5\times 5\times 5$ can be written as ${10}^3+5^3$.

Also, $10\times 10-10\times 5+5\times 5$ can be written as $({10}^2-10\times 5+5^2)$

Using the identity $(a^3+b^3)=(a+b)(a^2-ab+b^2)$,
we can say that $\frac{{10}^3-5^3}{{10}^2-10\times 5+5^2}=\frac{(10+5)({10}^2-10\times 5+5^2)}{{10}^2-10\times 5+5^2}=(10+5)=15$