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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