Question

Factorize each of the following algebraic expression:
x² − y² − 4xz + 4z²

Answer 1

$$\begin{gathered} {\mathrm{x}}^2-{\mathrm{y}}^2-4\mathrm{xz}+4{\mathrm{z}}^2 \\ =({\mathrm{x}}^2-4\mathrm{xz}+4{\mathrm{z}}^2)-{\mathrm{y}}^2 \\ =[{\mathrm{x}}^2-2\times \mathrm{x}\times 2\mathrm{z}+(2\mathrm{z}{)}^2]-{\mathrm{y}}^2 \\ =(\mathrm{x}-2\mathrm{z}{)}^2-{\mathrm{y}}^2 \\ =\left[\right(\mathrm{x}-2\mathrm{z})-\mathrm{y}]\left[\right(\mathrm{x}-2\mathrm{z})+\mathrm{y}] \\ =(\mathrm{x}-2\mathrm{z}-\mathrm{y})(\mathrm{x}-2\mathrm{z}+\mathrm{y}) \\ =(\mathrm{x}+\mathrm{y}-2\mathrm{z})(\mathrm{x}-\mathrm{y}-2\mathrm{z}) \end{gathered}$$