Simplify $ \dfrac {0.58 \times 0.58 \times 0.58 -0.001}{0.58 \times 0.58 +0.058 +0.01}$

Options
a) 0.28
b) 0.48
c) 0.42
d) 0.37

Solution

As per question
$ \dfrac {0.58 \times 0.58 \times 0.58 -0.001}{0.58 \times 0.58 +0.058 +0.01}$
$ \frac {0.58 \times 0.58 \times 0.58 -0.1 \times 0.1 \times 0.1}{0.58 \times 0.58 +0.58 \times 0.1 +0.1 \times 0.1}$
Let a = 0.58 , b = 0.1
$ \frac{a^3 – b^3}{a^2 + ab + b^2}$
a³ – b³ = (a-b) (a²+b²+ab)
$ \frac{a^3 – b^3}{a^2 + ab + b^2}$ = (a-b)
(a – b) = 0.58 – 0.1 = 0.48

Ans: b) 0.48