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Factorize each of the following algebraic expressions:  9z^2 – x^2 + 4xy – 4y^2

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Factorize each of the following algebraic expressions:

 9z2 – x2 + 4xy – 4y2

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As given,

9z2 – x2 + 4xy – 4y2

= (3z)2 – [x2 – 2 (x) (2y) + (2y)2]

= (3z)2 – (x – 2y)2

= [(x – 2y) + 3z] [–x + 2y + 3z)]

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