Expand
(i) (2a – 5b – 7c)2
(ii) (–3a + 4b – 5c)2
(iii)
(i) We know that,
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Using this formula, we get
= (2a)2 + (-5b)2 + (-7c)2 + 2(2a) (-5b) + 2 (-5b) (-7c) + 2 (-7c) (2a)
= 4a2 + 25b2 + 49c2 - 20ab + 70bc - 28ac
(ii) We know that,
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Using this formula, we get
= (-3a)2 + (4b)2 + (-5c)2 + 2(-3a) (4b) + 2 (4b) (-5c) + 2 (-5c) (-3a)
= 9a2 + 16b2 + 25c2 - 24ab - 40bc + 30ac
(iii) We know that,
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Using this formula, we get
= (1/2a)2 + (-1/4b)2 + (2)2 + 2(1/2a) (-1/4b) + 2 (-1/4b) (2) + 2 (2) (1/2a)
=