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Mathematics

4xy - x2 - 4y2 + z2

Factorisation

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Answer

Given,

   4xy - x2 - 4y2 + z2

= -[x2 + 4y2 - 4xy - z2]

= -[(x)2 + (2y)2 - 2 × x × 2y - (z)2]

= -[(x - 2y)2 - (z)2]

= (z)2 - (x - 2y)2

= (z + x - 2y)(z - x + 2y).

Hence, 4xy - x2 - 4y2 + z2 = (z + x - 2y)(z - x + 2y).

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