The value of $\frac{(2.7)^3-(2.2)^3}{(2.7)^2+2.7×2.2+(2.2)^2}$ is

0.5

The correct answer is Option (2) → 0.5

The expression is in the form:

$\frac{a^3 - b^3}{a^2 + ab + b^2}$

where:

• $a = 2.7$
• $b = 2.2$

We know the identity for the difference of cubes is:

$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

By rearranging this formula, we get:

$\frac{a^3 - b^3}{a^2 + ab + b^2} = a - b$

Substituting the values of $a$ and $b$ back into the simplified expression:

$\text{Value} = 2.7 - 2.2$

$\text{Value} = 0.5$