Practical Elementary Algebra

Practical Elementary Algebra

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1908 edition. Excerpt: ... b). Solution, (a-ft)4 = a'-4a3b + i--? a2b2--ab3 + i-1 64 v' 2 3 4 = a4-4 a3b + 6 a2b2-4 ab + b Check. Let a = 3, & = 1. Then, (3-l)4 = 24 = 16; also a4-4 a3b + (i a2b2-4 ab3 + b = 81-108 + 54-12 + 1 = 16. 3. Expand (a--bf by Newton's binomial theorem and compare the result with that given on p. 220 in Ex. 1. Similarly expand (x--yf and compare the coefficients and exponents with those given on p. 220. Expand in the following problems and check as in Ex. 2 until the process of checking is well understood. 4. (a + 6)4; a-bj; (x + y); (m + nf; (p-q)w. 5. Develop (3 m2--2 w)4 by Newton's binomial theorem. Solution. Notice that 3 m2 takes the place of A and 2 re that of B. To preserve the exponents of A and B for use in getting coefficients it is necessary to write 3 m? and 2 re in parentheses. (3 ---2 n) = (3 m2)4-4 (3 m2)8(2 n)+i-? (3 m2)2(2 n)2-52 (3 m) (2 n)8 + (2 -)4 = 81 m---216 m'n + 216 m-2-96 m?n-+16 nK ( 27) To check the result let m = 2, n = 1. Then, (3 m2-2 n)4 = 10,000; also 81 m8-216 nfin + 216 ra4ra2-96mV + 16 re4 = 20736-13824 +3456-384 + 16 = 10000. a. In the preceding solution we think of (2 m2--3 re) as written 2 m2--(+ 3 re). If we wrote it 2 m2 + (--3 -) all the signs between terms would be 4-, and--3 re instead of + 3re would appear in parenthesis each time. The results would be the same. 6. (2a + 5 by. 7. (2x + 3y). 8. (xy-2abf. 9. (4a2c2+5c3)3. 10. (3 a2-5 b2)4. 11. (a2-4)4. 12. (2a2&-7c3)4. 13. (9 x7-4 y6)3. 14. (ia-3 6)4. b. Let the student write down the values of (a + ft)2, (a + ft)3, (a + ft)4, (a + 6)5, (a + 6)6, and memorize the binomial coefficients, so that he will not have to calculate them each time. Thus, the binomial coefficients for the fourth power are 1, 4, 6, ...show more

Product details

  • 12-17
  • Paperback | 76 pages
  • 189 x 246 x 4mm | 154g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236548558
  • 9781236548559