Given expression
\(\begin{aligned}
\sqrt[3]{x^2+64}-\sqrt[3]{x^2+27} & =4\left(1+\frac{x^2}{64}\right)^{1 / 3}-3\left(1+\frac{x^2}{27}\right)^{1 / 3} \\
& =4\left[1+\frac{x^2}{3 \times 64}\right]-3\left[1+\frac{x^2}{3 \times 27}\right]
\end{aligned}\)
\{on neglecting \(x^4\) and higher powers of \(x\) \}
\(\begin{aligned}
& =4+\frac{x^2}{48}-3-\frac{x^2}{27}=1+\frac{27-48}{48 \times 27} x^2 \\
& =1-\frac{21}{48 \times 27} x^2=1-\frac{7}{432} x^2
\end{aligned}\)
Hence, option (b) is correct.