# 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
• Miami Fl, United States
• English
• black & white illustrations
• 1236548558
• 9781236548559