Evaluate:

$\dfrac{0.8 \times 0.8 \times 0.8 + 0.5 \times 0.5 \times 0.5}{0.8 \times 0.8 - 0.8 \times 0.5 + 0.5 \times 0.5}$

Given,

$\Rightarrow \dfrac{0.8 \times 0.8 \times 0.8 + 0.5 \times 0.5 \times 0.5}{0.8 \times 0.8 - 0.8 \times 0.5 + 0.5 \times 0.5} \\[1em] \Rightarrow \dfrac{(0.8)^3 + (0.5)^3}{(0.8)^2 + (0.5)^2 - 0.8 \times 0.5}$

Using the formula, (a³ + b³) = (a + b)(a² - ab + b²)

$= \dfrac{(0.8 + 0.5)[(0.8)^2 + (0.5)^2 - 0.8 \times 0.5]}{(0.8)^2 + (0.5)^2 - 0.8 \times 0.5}\\[1em] = (0.8 + 0.5)\\[1em] = 1.3$

Hence, $\dfrac{0.8 \times 0.8 \times 0.8 + 0.5 \times 0.5 \times 0.5}{0.8 \times 0.8 - 0.8 \times 0.5 + 0.5 \times 0.5}$ = 1.3.