Please answer these questions

(1).

$$\begin{gathered} 4{\mathrm{x}}^2 - 4\mathrm{xy} + {\mathrm{y}}^2 - 9{\mathrm{z}}^2 \\ =\left[4{\mathrm{x}}^2 - 4\mathrm{xy} + {\mathrm{y}}^2\right] - {\left(3\mathrm{z}\right)}^2 \\ =\left[{\left(2\mathrm{x}\right)}^2 - 2\left(2\mathrm{x}\right)\left(\mathrm{y}\right) + {\mathrm{y}}^2\right] - {\left(3\mathrm{z}\right)}^2 \\ ={\left(2\mathrm{x} - \mathrm{y}\right)}^2 - {\left(3\mathrm{z}\right)}^2 \left[\mathbf{as}\mathbf{,}\mathbf{ }{\mathbf{a}}^{\mathbf{2}}\mathbf{ }\mathbf{-}\mathbf{ }\mathbf{2}\mathbf{ab}\mathbf{ }\mathbf{+}\mathbf{ }{\mathbf{b}}^{\mathbf{2}}\mathbf{ }\mathbf{=}\mathbf{ }{\left(\mathbf{a}\mathbf{-}\mathbf{b}\right)}^{\mathbf{2}}\right] \\ =\left(2\mathrm{x} - \mathrm{y} + 3\mathrm{z}\right)\left(2\mathrm{x} - \mathrm{y} - 3\mathrm{z}\right) \left[\mathbf{as}\mathbf{,}\mathbf{ }{\mathbf{a}}^{\mathbf{2}}\mathbf{ }\mathbf{-}\mathbf{ }{\mathbf{b}}^{\mathbf{2}}\mathbf{ }\mathbf{=}\mathbf{ }\left(\mathbf{a}\mathbf{+}\mathbf{b}\right)\left(\mathbf{a}\mathbf{-}\mathbf{b}\right)\right] \end{gathered}$$


(3).

$$\begin{gathered} {\mathrm{x}}^2 + 12\mathrm{x} - 45 \\ ={\mathrm{x}}^2 + 15\mathrm{x} - 3\mathrm{x} - 45 \\ =\mathrm{x}\left(\mathrm{x} + 15\right) - 3\left(\mathrm{x} + 15\right) \\ =\left(\mathrm{x} - 3\right)\left(\mathrm{x} + 15\right) \end{gathered}$$

Kindly ask the remaining queries in different threads.