Q. 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 $(a-b)\left(a^2+a b+b^2\right)=a^3-b^3$. (D) $\Rightarrow x^{\frac{2}{3} \times 3}-y^{\frac{2}{3} \times 3}=x^2-y^2$.
Polynomials, LCM and HCF of Polynomials
Solution: