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Question
Factorize a2 + 4b2 - 4ab - 4c2
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Solution
On rearranging
= a2 - 4ab + 4b2 - 4c2
= (a)2 - 2 x a x 2b + (2b)2 - 4c2
Using identity a2 - 2ab + b2 = (a - b)2
= (a - 2b)2 - 4c2
= (a - 2b)2 - (2c)2
Using identity a2 - b2 = (a + b)(a - b)
= (a - 2b + 2c)(a - 2b - 2c)
∴ a2 + 4b2 - 4ab - 4c2 = (a - 2b + 2c)(a - 2b - 2c)
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