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Question
Expand the following:
(2a − 5b − 6c)2
Sum
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Solution
(2a − 5b − 6c)2
Using the identity:
(a − b − c)2 = a2 + b2 + c2 − 2ab + 2bc − 2ac
Here, let a = 2a, b = 5b, c = 6c
(2a − 5b − 6c)2 = (2a)2 + (5b)2 + (6c)2 − 2(2a) (5b) + 2(5b) (6c) − 2(2a) (6c)
= 4a2 + 25b2 + 36c2 − 2(10ab) + 2(30bc) − 2(12ac)
∴ (2a − 5b − 6c)2 = 4a2 + 25b2 + 36c2 − 20ab + 60bc − 24ac
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