EXAMPLES III. a.
Find the sum of
1. a + 2/j-3^; -3a + 5+2c;2rt-36 + c. 2. 3a + 26-c; -a + 3& + 2c;2a-6 + 3c. 3. -Sx--2y + z; x-Sy-h2z; 2x + y -3z. 4. -x + 2y + Sz; Sx- y + 2z; 2x-hSy -z. 5. 4« + 36 + 5c; - 2a + Sb -Sc ; a - b + c. 6. - 15 a - 19 6 - 18 c ; 14 a + 15 6 + 8 c ; a-h 51 ±9c. 7. 25 a - 15 & + c ; 13 « ~ 10 & + 4 c ; a + 20 6 - c. 8. -16a-105 + 5r; lOa + 56 + c; 6a + 55-c. 9. 5ax — 7by+cz; ax + 2by — cz; —oax+2by--o cz. 10. 20 p + q- r ; p -20q-{- r; 2^ + q -20r.
Add together the following expressions
11. - 6ab -{-6bc-7 ca; 8 r/6 - 4 6c + 3 ca ; - 2 «6 - 2 6c + 4 ca. 12. loa6-275c-6ca ; 14rt6-186c+10cff ; -49 a6 + 45 6c-3ca. 13. 5 a6 + 6c — 3 ca ; «6 — 6c + ca ; — a6 + 6c + 2 cd. 14. pq + qr - rp ; - pq + qr + rp ; i)g - qr + rp. 15. x-- y -- z; 2x + Sy -2z; Sx- 4:y + z. 16. 2a-36 + c; 15 a- 21 6 -8c; 3a + 24 6 + 7c. 17. ixy — 9yz -- 2 zx ; — 25 xy --2yz — zx ; 23 xy — lo yz + zx. 18. 17 a6 - 13 6c + 8 ca ; - 5 a6 + 9 6c - 7 ca ; 2 a6 - 7 6c - ca. 19. 47a;-63y + ^; -25x+15y-32; -22x + 48y + Ibz. 20. 23a-176-2c; -9a + 156 + 7c; -13a+36-4c.
DIMENSION, DEGREE, ASCENDING AND DESCENDING POWERS.
29. Each of the letters composing a term is called a dimension of the term, and the number of letters involved is called the degree of the term. Thus the product abc is said to be of three dimensions, or of the third degree; and ax^4 is said to be of five dimensions, or of the fifth degree.
A numerical coefficient is not counted. Thus 8a2b5 and a2b5 are each of seven dimensions, or of the seventh degree.
But it is sometimes useful to speak of the dimensions of an expression with regard to any one of the letters it in-
