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30 Rh If a 4, b sh @ 1, f=0, x=4, y =1, find the value of

21. 3a?+ bx —Acy. 24. 8a7y? — 5 Dx — 28. 22. 2ab? — 3 be? + 2 fe. 25. 203-38 b3 + Tey}. 23. fa? — 253 — ca’. 26. 3by! — 403 — 6ctx.

27. 2,/(ac) — 3,/ (ay) + / (Wc).

28. 3,/(acx) — 2,/(b?y) — 6/(c*y).

29. 7,/(a%) — 3,/(btc2) + 5/ (S22).

80. 3c¢,/(8 be) — 5/4 cy?) — 2 ey/(8 be).

46. The following examples further illustrate the rule of signs and the law of indices.

Ex. 1. Multiply 4a by — 3b.

By the rule of signs the product is negative ; also 4a x 3b = 12 ab.

4a x(—3b)=— 12 ab.

Ex. 2. Multiply — 5abx by — ab3x.

Here the absolute value of the product is 5 abx, and by the rule of signs the product is positive.

(— 5 ab3x) x (— ab3x) = 5 abx.

Ex. 3. Find the continued product of 3 ab, — 2 ab, — ab.

This result, however, may be written down at once; for

3a2b x 2ab x abb = 6 ab, and by the rule of signs the required product is positive.

3ab x (— 2.a3b) = — 6 ab3 ; (— 6 ab) x (— ab) = + 6 a8b7.

Thus the complete product is 6 ab7.

Ex. 4. Multiply 6 a3 — 5a2b — 4ab by — 3ab.

The product is the algebraic sum of the partial products formed according to the rule enunciated in Art. 40 ;

thus (6 a3 — 5ab— 4 ab) x (— 3 ab) = — 18 ab + 15 ab+ 12 ab.

EXAMPLES IV. c.

Multiply together 1. ax and — 3 ax. 2. —2abx and — 7abx. 3. ab and — ab. 4. 6xy and — 10xy. 5. — abcd and — 3 abcd. 6. xyz and — 5 xy3z. 7. xy +4 yz and — 12 xyz. 8. ab — bc and abc8.