Page:Elementary algebra (1896).djvu/49

31 Rh 9. —x—y—zand — 3x. 12. —2ab —4ab and — 7ab. 10. a — b + c and abc. 18. 5xy — xy + 8xy and 3xy. 11. — ab + bc — ca and — abc. 14. — 7 xy— xy and — 8x3y3.

16. —x2yz + dxy2z — 8xyz and xyz.

16. 4xyz — 8xyz and — 12x3yz3. 18. 8xyz — 10 x3yz3 and — sxyz. 17. — 13 xy — 15xy and — 7x3y8. 19. abc — a2bc — abc and — abc. 20. — abc + bca — cab and — ab.

Find the product of

21. 2a—3b+4c and — 3a. 23. 2a b—c and 2ax.

22. 8x—2y—4 and — x. 24. 5ax — 3ax3 and — ax. 25. — 30ax and — 3a^2 + ax — 3x^2.

26. — xy and — 3x + xy. 27. — xy and — 1x^2 + 2y^2.

47. The results of Art. 41 may be extended to the case where one or both of the expressions to be multiplied together contain more than two terms. For instance

(a—b+c)m=am—bm +cm; replacing m by x— y, we have (a—b+c)(x—y)= a(x— y)—b(x— y) + c(x — y) = (ax — ay) — (bx — by) + (cx — cy) = ax — ay — bx + by + cx — cy.

48. These results enable us to state the general rule for multiplying together any two compound expressions.

Rule. Multiply each term of the first expression by each term of the second. When the terms multiplied together have like siqns, prefix to the product the sign +, when unlike prefix —; the algebraic sum of the partial products so formed gives the complete product.

This process is called Distributing the Product.

Ex. 1. Multiply x + 8 by x +7.

x+ 8 x+ 7 x^2+ 8x + 7x +56

by addition x^2+ 15x + 56