Mathematics
(a2 + b2 - 4c2)2 - 4a2b2
Factorisation
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Answer
Given,
(a2 + b2 - 4c2)2 - 4a2b2
= (a2 + b2 - 4c2)2 - (2ab)2
= (a2 + b2 - 4c2 + 2ab)(a2 + b2 - 4c2 - 2ab)
= (a2 + b2 + 2ab - 4c2)(a2 + b2- 2ab - 4c2)
= [(a + b)2 - (2c)2][(a - b)2 - (2c)2]
= (a + b + 2c)(a + b - 2c)(a - b + 2c)(a - b - 2c).
Hence, (a2 + b2 - 4c2)2 - 4a2b2 = (a + b + 2c)(a + b - 2c)(a - b + 2c)(a - b - 2c).
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