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Question
Factorize each of the following algebraic expression:
x2 − y2 − 4xz + 4z2
Solution
\[x^2 - y^2 - 4xz + 4 z^2 \]
\[ = ( x^2 - 4xz + 4 z^2 ) - y^2 \]
\[ = [ x^2 - 2 \times x \times 2z + (2z )^2 ] - y^2 \]
\[ = (x - 2z )^2 - y^2 \]
\[ = [(x - 2z) - y][(x - 2z) + y]\]
\[ = (x - 2z - y)(x - 2z + y)\]
\[ = (x + y - 2z)(x - y - 2z)\]
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