Question 5: \((iv)\) \(\quad\) \(\left( a^{\frac{1}{3}} +b^{\frac{2}{3}}\right) \times \left( a^{\frac{2}{3}} -a^{\frac{1}{3}} b^{\frac{2}{3}} +b^{\frac{4}{3}}\right)\)
Solution:
\[ \begin{align*}
&= \left( a^{\frac{1}{3}} + b^{\frac{2}{3}} \right) \times \left( a^{\frac{2}{3}} – a^{\frac{1}{3}} b^{\frac{2}{3}} + b^{\frac{4}{3}} \right) \\
&= \left( a^{\frac{1}{3}} \right)^3 + \left( b^{\frac{2}{3}} \right)^3\\
&= a + b^{\frac{2}{3}} \\
& \text{since } a^3 + b^3 = (a+b)(a^2 – ab + b^2) \text{} \\
\end{align*} \]