Question

The polynomial x² + y² – z² – 2xy on factorization gives _____________.

Answer 1

$$\begin{gathered} x^2+y^2-z^2-2xy \\ =\left(x^2+y^2-2xy\right)-z^2 \\ ={\left(x-y\right)}^2-{\left(z\right)}^2\left(\mathrm{Using}\mathrm{the}\mathrm{identity}:{\left(a-b\right)}^2=a^2+b^2-2ab\right) \\ =\left(x-y+z\right)\left(x-y-z\right)\left(\mathrm{Using}\mathrm{the}\mathrm{identity}:a^2-b^2=\left(a+b\right)\left(a-b\right)\right) \end{gathered}$$

Hence, the polynomial x² + y² – z² – 2xy on factorization gives $\underline{\left(x-y+z\right)\left(x-y-z\right)}$.