1. Multiply

III. MULTIPLICATION.

(1) x2+2xy-312 by x2-5xy+4y2.
(2) 1+x+x+25 by 1-x+x2 — x3.
(3) x^+x3y—x2y2+xy3 +ya by x—y.
(4) 4ab-2ac by 6ab+3ac+8bcd.
(5) 2a(x+y)—bz by 3b(x−2)+2ay.
(6) a2 + a2x2 + x2" by 2a"-2x".

n

2n

(7) am+bm by a"-b".

(8) a3—a‡b3+b3 by a§+b§.

(9) x3—yś by x3⁄4+xšyš+yš.

(10) x3yś—x3⁄4y +x3yś by x3⁄4y−š+x $yš.
(11) x+2y++38 by x−2y+38§.

(12) 2x2—§x+1 by x2—1x.

(15) 4a−6b(~ +b) + 3ab by 6b2 —4a.

(16) 3ax-1—(2a3x ̄ŝ+1) by (2aŝx−ŝ—1)—a§x ̄§. (17) 1x+12m+ly−1+÷xm+2y−2+xm+3y=3

-1

by 8x2+161⁄23y−1+32x1y−2.

(18) x3-(a+b+c)x2 + (bc+ca+ab)x— abc
by x-a.

(19) x2-(a—b)x-ab by x2 + (a-b)x-ab.

(3) 2x−m, 2x+n, x+2m, x−2n.

(4) 3x− 1, x2+1, 3x+1.

(5) (a+b+c) (a+b−c) (a+c—b) (b+c−a).
(6) x-a, x+a, x2 + ax+ a2, x2-ax+a2.

(7) x*+y3, x¤—x$y$+x$y$—yễ, x+y.

4. Multiply x3-ax2+ bx-c by x2+mx+n, and arrange in brackets the coefficients of like powers of x.

5. Find the coefficient of x3 in the product of

x3 — bx2— 3abx+a2 and 2x2-3ax-b2,

and the coefficient of x in the continued product of x−3m, x+2n, 2x−n, 3x+m.

1, Divide

IV. DIVISION.

(1) x3 — 4x3y2 — 8x2μ3 — 17xya — 1235

by x2-2x-3y2.

(2) x+2x1—7x2- 16 by x3+2x2+3x+4.

(3) x6-2a3x3+a6 by x2-2ax+a2.

(4) a5 — a3b2+2a2b3—ab1+b5 by a2—ab+b3. (5) a2+ab+2ac-262+7bc-3c2 by a-b+3c. (6) a2+2ac-2bd-b2+c2-d2 by a-b+c-d. (7) a3 + b3+c3-3abc by a+b+c. (8) 1+x3−8y3+6xy by 1+x−2y. (9) x1—9x2-6xy—y2 by x2+3x+y. (10) 1−6x5+5x6 by 1−2x+x2.

(11) ax3 — (a2+b2)x2 + b2 by ax—b.

(12) 2abx2 - (3bc—2ad)xy—3cdy2 by bx+dy.

(13) x5—1—p(x1 −x)+q(x3 —x2) by x−1.

́(14) m3nx1+(2m2 — 3n2) (m2x3y — 3mnx2y2+9n2xy3) — 54mn3y1 by nx+2my.

(15) 2a31 — 6a2 fn +бanf2n — 2b3n by aa —b”.

(16) prxm+n+qrx2n — (r2 —pq)x2 + p2x2 -pr by rx"+p.

(17) 2ak — 3a§b§— 2a§b$+3b by aa—b§. (18) x+xłyk+y by xì—xłyś+ył.

(19) a3+3a2x-2x3 by 1a+x.

(22) -5a2+11ab-1ac + 15 b2+25bc by a−56. (23) 1x3+x2+3x+1 by 1x+1.

(25) (2x2−7x+6)aa + (x2−7x+7)a3 — (3x+4)a3

-(x+7)a−2 by (x−2)a2—3a—I.

2. Divide

(1) a by 1+ 2x to four terms.
(2) a by 1+5x to five terms.

(3) x-a by x-b to three terms.

3. Divide 813-13 by (2x-1)2, writing the remainder as a fraction.

4. Divide r3 by 1-2 to three terms. What is the difference between your answer and the true one?

5. Find the difference between

I

-x

I+x+x2+x3 + &c.+x2-1.

x

and

6. Find the value of to four terms, and the re

I-X

mainder, when n terms of the quotient have been taken.

7. Write down the quotients of

(1) 49x2-2572 divided by 7x-5y.

(6) x6-a6

36

36

36

2n

am ban-c3p.

a2x2-abxy+b2y2.

3x-a.

x-a, x+a, x3 — a3, x3+a3, severally.

(7) 4-2 by 2zł-2. (8)+3 by y +

—b3 by b2 (10) al—bî by at—b‡.

8. Shew that a"-b" is always divisible by a-b.

9. Under what conditions will a"+x" divide by a+x without remainder? Write down the first three and the last three terms of the quotient.

10. Prove that amn-bmn is divisible by both am — bm and a"-b", and give the first and second terms and the ast and last but one in each quotient.

2. Arrange according to descending powers of x, collecting the coefficients of each power into brackets,

x3-ax-c2x2-bx+ bx3-cx2 + a2x3 — x2-cx.