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Question
Factorize each of the following algebraic expression:
9z2 − x2 + 4xy − 4y2
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Solution
\[9 z^2 - x^2 + 4xy - 4 y^2 \]
\[ = 9 z^2 - ( x^2 - 4xy + 4 y^2 )\]
\[ = 9 z^2 - [ x^2 - 2 \times x \times 2y + (2y )^2 ]\]
\[ = (3z )^2 - (x - 2y )^2 \]
\[ = [3z - (x - 2y)][3z + (x - 2y)]\]
\[ = (3z - x + 2y)(3z + x - 2y)\]
\[ = (x - 2y + 3z)( - x + 2y + 3z)\]
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