Factorize each of the following algebraic expression:

Question:

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

Solution:

$x^{2}-y^{2}-4 x z+4 z^{2}$

$=\left(\mathrm{x}^{2}-4 \mathrm{xz}+4 \mathrm{z}^{2}\right)-\mathrm{y}^{2}$

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

$=(\mathrm{x}-2 \mathrm{z})^{2}-\mathrm{y}^{2}$

$=[(\mathrm{x}-2 \mathrm{z})-\mathrm{y}][(\mathrm{x}-2 \mathrm{z})+\mathrm{y}]$

$=(\mathrm{x}-2 \mathrm{z}-\mathrm{y})(\mathrm{x}-2 \mathrm{z}+\mathrm{y})$

$=(\mathrm{x}+\mathrm{y}-2 \mathrm{z})(\mathrm{x}-\mathrm{y}-2 \mathrm{z})$

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