Elementary Algebra First Second Year Course volume 1

Cover Elementary Algebra First Second Year Course volume 1
Elementary Algebra First Second Year Course volume 1
Florian Cajori
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17. 125 c 2 d 2 + 100 c 2 cP - 150 c 3 ^.
18. 15 & 3 0/i 2 + 17 bgW-Wtfh - 19. A n & a"c a n d.
20. 2 a?" 6 &ic + 4 cof.
21. 3 a"6 n c 9 a n b n cd + 6 a n b"ce.
22. Cy^-dy^ + gy*".
23. 5 a 2 6 n + 10 a s &" 15 a 4 &". 24.
116. II. Type form : or + ay + bx + &y.
Group the first two terms together and the last two terms together. Then factor each group. Notice that the factoring should reveal the same binomial or polynomial factor in all the groups.
We obtain (ax + ay) + (bx + by) = a(x + y ) +
...6(z + y).
Divide by x + y and we obtain the quotient a + b. Taking the divisor x + y as one factor, and the quotient a + b as the other factor, we have ox + ay + bx + by = (x +y)(a + b).
Factor 2 a - 66 - ad + 3bd.
Grouping, (2 a - 6 6) - (ad - 3 bd). Factoring each group, 2 (a 3 6) d(a 3 b). The factor a 3 b is seen to occur in both groups. Dividing by a 3 6, we obtain 2 d.
Taking the divisor a 3 b as one factor, and the quotient 2 d as an- other factor, we have 2 a - 6 b - ad + 3 bd =(a - 3 6)(2 - d).


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