Expand each of the following, using suitable identities
(-2a + 5b - 3c)2
(-2a + 5b - 3c)2 = [(-2a) + (5b) + (-3c)]2
Using (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
Here x = -2a, y = 5b and z = -3c
⇒ (-2a + 5b - 3c)2 = (-2a)2 + (5b)2 + (-3c)2 + 2(-2a)(5b) + 2(5b)(-3c) + 2(-3c)(-2a)
⇒ (-2a + 5b - 3c)2 = 4a2 + 25b2 + 9c2 + (-20ab) + (-30bc) + 12ac
⇒ (-2a + 5b - 3c)2 = 4a2 + 25b2 + 9c2 - 20ab - 30bc + 12ac
Therefore
(-2a + 5b - 3c)2 = 4a2 + 25b2 + 9c2 - 20ab - 30bc + 12ac
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