Factorize each of the following algebraic expression:
9z² − x² + 4xy − 4y²

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Solution

$9 z^{2} - x^{2} + 4 x y - 4 y^{2} = 9 z^{2} - (x^{2} - 4 x y + 4 y^{2}) = 9 z^{2} - [x^{2} - 2 \times x \times 2 y + (2 y)^{2}] = (3 z)^{2} - (x - 2 y)^{2} = [3 z - (x - 2 y)] [3 z + (x - 2 y)] = (3 z - x + 2 y) (3 z + x - 2 y) = (x - 2 y + 3 z) (- x + 2 y + 3 z)$

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