derive any 10 basic algebraic identities

Dear student
Kindly refer the  link for your query.
https://www.meritnation.com/ask-answer/question/state-all-the-algebraic-identities-from-polynomials/math/10632147 
Proof:
$$\begin{gathered} \mathrm{Consider} \\ 1){\left(\mathrm{x}+\mathrm{y}\right)}^2 \\ =\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}+\mathrm{y}\right) \\ ={\mathrm{x}}^2+\mathrm{xy}+\mathrm{xy}+{\mathrm{y}}^2 \\ ={\mathrm{x}}^2+2\mathrm{xy}+{\mathrm{y}}^2 \\ 2) {\left(\mathrm{x}-\mathrm{y}\right)}^2 \\ =\left(\mathrm{x}-\mathrm{y}\right)\left(\mathrm{x}-\mathrm{y}\right) \\ ={\mathrm{x}}^2-\mathrm{xy}-\mathrm{xy}+{\mathrm{y}}^2 \\ ={\mathrm{x}}^2-2\mathrm{xy}+{\mathrm{y}}^2 \\ 3) \left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}-\mathrm{y}\right) \\ ={\mathrm{x}}^2-\mathrm{xy}+\mathrm{xy}-{\mathrm{y}}^2 \\ ={\mathrm{x}}^2-{\mathrm{y}}^2 \end{gathered}$$
Similarly try others.
Regards