Expand:
(i) (a + 2b + 5c)2
(ii) (2a – b + c)2
(iii) (a – 2b – 3c)2
(i) We know that,
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Using this formula, we get
= (a)2 + (2b)2 + (5c)2 + 2(a) (2b) + 2 (2b) (5c) + 2 (5c) (a)
= a2 + 4b2 + 25c2 + 4ab + 20bc + 10ac
(ii) We know that,
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Using this formula, we get
= (2a)2 + (-b)2 + (c)2 + 2(2a) (-b) + 2 (-b) (c) + 2 (c) (2a)
= 4a2 + b2 + c2 - 4ab - 2bc + 4ac
(iii) We know that,
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Using this formula, we get
= (a)2 + (-2b)2 + (-3c)2 + 2(a) (-2b) + 2 (-2b) (-3c) + 2 (-3c) (a)
= a2 + 4b2 + 9c2 - 4ab + 12bc - 6ac