Q. Factorise
$a^2-b^2-{\left(a+b\right)}^2$

Dear Student,
Here is the solution of your asked query:
$$\begin{gathered} {\mathrm{a}}^2-{\mathrm{b}}^2-{\left(\mathrm{a}+\mathrm{b}\right)}^2 \\ =\left(\mathrm{a}-\mathrm{b}\right)\left(\mathrm{a}+\mathrm{b}\right)-{\left(\mathrm{a}+\mathrm{b}\right)}^2 \\ =\left(\mathrm{a}+\mathrm{b}\right)\left[\left(\mathrm{a}-\mathrm{b}\right)-\left(\mathrm{a}+\mathrm{b}\right)\right] \\ =\left(\mathrm{a}+\mathrm{b}\right)\left[\mathrm{a}-\mathrm{b}-\mathrm{a}-\mathrm{b}\right] \\ =\left(\mathrm{a}+\mathrm{b}\right)\left(-2\mathrm{b}\right) \\ =-2\mathrm{b}\left(\mathrm{a}+\mathrm{b}\right) \end{gathered}$$
Regards