Question

The polynomial , x⁶ + 64y⁶ on factorization gives _____________.

Answer 1

$$\begin{gathered} x^6+64y^6 \\ ={\left(x^2\right)}^3+{\left(4y^2\right)}^3 \\ =\left(x^2+4y^2\right)\left({\left(x^2\right)}^2+{\left(4y^2\right)}^2-\left(x^2\right)\left(4y^2\right)\right)\left(\mathrm{Using}\mathrm{the}\mathrm{identity}:a^3+b^3=\left(a+b\right)\left(a^2+b^2-ab\right)\right) \\ =\left(x^2+4y^2\right)\left(x^4+16y^4-4x^2{y}^2\right) \end{gathered}$$

Hence, the polynomial x⁶ + 64y⁶ on factorization gives $\underline{\left(x^2+4y^2\right)\left(x^4+16y^4-4x^2{y}^2\right)}$.