University Algebra

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Here r = 8, n = 11 ; hence, the 8thtom = 1 l:2°3 9 4 8 5. 6 6 7 5 , (- 2t -)' = 330 (81 a 2 ) (- 128 b~'') = - 3421440 a 2 J- 7, ^ras.
Note. The note to Ex. 4, Art. 403, applies with equal force to examples in this article.
EXAMPLES.
Find the 2. 10th term of (a + x) 15 . 5. 5th term of (1 - a 2 ) 12 .
3. 6th term of (1 + m) u . 6. 9th term of (x~ 1 -2 y*) u .
4. 8th term of (c - d) l \ 7. 8th term of (a% + 3 x" 1 ) 10 .
405. A trinomial may he raised to any power by the Bi- nomial Theorem, if t
...wo of its terms he enclosed in a paren- thesis and regarded as a single term ; the operations indicated being performed after the expansion by the Theorem has been effected.
1. Expand (2 a — b + c 2 ) 3 by the Binomial Theorem.
(2 a - b + c 2 ) 3 = [(2 a-b) + (c 2 )] 3 = (2 a - by + 3 (2 a -b) 2 (c 2 ) + 3 (2 a - b) (c 2 ) 2 + (c 2 ) 3 =Sa 3 ~12a 2 b + 6ab 2 -b 3 +3c 2 (4:a 2 -4ab + b 2 ) + 3c 4 (2a-b) + c 6 = 8 a 3 - 12 a 2 b + 6 a b 2 - b 3 + 12 a 2 c 2 - 12 a b c 2 + 3 b 2 c 2 + 6ac i -3bc 4 + c 6, Ans.


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