Mathematics
4x2 - 12ax - y2 - z2 - 2yz + 9a2
Factorisation
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Answer
Given,
4x2 - 12ax - y2 - z2 - 2yz + 9a2
= 4x2 - 12ax + 9a2 - y2 - z2 - 2yz
= (2x)2 - 2 × 2x × 3a + (3a)2 - (y2 + z2 + 2yz)
= (2x - 3a)2 - (y + z)2
= (2x - 3a + y + z)[2x - 3a - (y + z)]
= (2x - 3a + y + z)(2x - 3a - y - z).
Hence, 4x2 - 12ax - y2 - z2 - 2yz + 9a2 = (2x - 3a + y + z)(2x - 3a - y - z).
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