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Problem 6 - Entrance Test
Expand (2a - 3b + c)^2.
A. 4a^2 + 9b^2 + c^2 - 12ab + 6bc - 4ca
B. 4a^2 + 9b^2 + c^2 - 12ab - 6bc + 4ca
C. 4a^2 + 9b^2 + c^2 - 12ab + 6bc + 4ca
D. 4a^2 + 9b^2 + c^2 + 12ab - 6bc - 4ca
Check Answer
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Correct: B
Using the identity (x+y+z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx, here x = 2a, y = -3b, z = c. So, (2a - 3b + c)^2 = (2a)^2 + (-3b)^2 + (c)^2 + 2(2a)(-3b) + 2(-3b)(c) + 2(c)(2a) = 4a^2 + 9b^2 + c^2 - 12ab - 6bc + 4ca.