Question

Simplify $\left(x^{\frac{2}{3}}-y^{\frac{2}{3}}\right)\left(x^{\frac{4}{3}}+x^{\frac{2}{3}}{y}^{\frac{2}{3}}+y^{\frac{4}{3}}\right)$ The following steps are involved in solving the above problem. Arrange them in sequential order. \begin{array}{l} \therefore\left(x^{\frac{2}{3}}-y^{\frac{2}{3}}\right)\left[\left(x^{\frac{2}{3}}\right)^2+x^{\frac{2}{3}} y^{\frac{2}{3}}+\left(\frac{2}{y^3}\right)^2\right] \\ =\left(\frac{2}{x^{\frac{2}{3}}}\right)^3-\left(\frac{2}{y^3}\right)^3 \end{array} (A) (B) Given expression can be written as \left(x^{\frac{2}{3}}-y^{\frac{2}{3}}\right)\left[\left(\frac{2}{x^3}\right)^2+x^{\frac{2}{3}} y^{\frac{2}{3}}+\left(y^{\frac{2}{3}}\right)^2\right] (C) We have $(a-b)\left(a^2+ab+b^2\right)=a^3-b^3$. (D) $\Rightarrow x^{\frac{2}{3}\times 3}-y^{\frac{2}{3}\times 3}=x^2-y^2$.

• A. $ABCD$
• B. DBAC
• C. $BADC$
• D. $BCAD$

Answer 1

Answer: (D)

$(B),(C),(A)$ and $(D)$ is the required sequential order.