Page:Elementary algebra (1896).djvu/45

27 Rh Ex. 3(2a+3b-4c)=6a+ 9b—12c. (4x^2 —7y —8z^2) x 3xy^2= 12 x^3y^2 — 21 xy^3— 24 xy^2z^3,

Note. It should be observed that for the present a, b,c, m denote positive whole numbers, and that a is supposed to be greater than b.

EXAMPLES IV. a.

Find value of

1. a x 12. 6. 2abe x 8ac3. 11. <y? x Cart. 2. 40x 5a’. to BOUP <A, 12. abe x xyz. 3. Tab x 8 ab. 8. 5a7b x 2a. 13. 3.Wbix3 x 5 abbe. 4. Guy? x 523. 9. 4070? x 7a. 14. 4 abe x 7 b2ct. 5. 8@b x BP. 10. 5a*l3 x 22y?. 16. Sax x 8 cx. Multiply

16. 523y8 by 6 a323. 21. 544 38y by 222.

17. 2a°y by a5y7. 22. a2? +b2?—¢ by abd.

18. 3aeaty™ by ay. 23. be + ca—ab by abe.

19. ab + be by ab. 24. 64 8)2—2¢2 by 4a%c3,

20. S5ab—7bx by 4.07bz3. 25. 5a?y + xy? — 7 ay? by 323.

MULTIPLICATION OF COMPOUND EXPRESSIONS.

42. If in Art. 41 we write c +d for m in (1), we have

(a+ b)(c+d)=a(c + d )+b(c+d) =(c+d)a+(c+d)b [Art. 37.] =ac+ ad + bc + bd.

Again, from (2 (a- b)(c+d)=a(c + d )-b(c+d) =(c+d)a-(c+d)b [Art. 37.] =ac+ ad - bc - bd.

Similarly, by writing c-d for m in (1) (a+ b)(c-d)=a(c - d )+b(c-d) =(c-d)a+(c-d)b [Art. 37.] =ac- ad + bc - bd.