(3) Simplify (a+b+c)(b+c−a)+(a+b−c)
(a+c-b).

(4) Divide 3+(a+b+c) x2+(bc+ac+ab)x+abc
by x2+ax+bx+ab.

11. Resolve into factors—

(1) (3a+2b-c-d)2+(3a-b-c)2

-(c+d-3a-2b)2-(a-3b-c)3.

(2) (x-2y)-(y-2x)3.

(3) 2x2-(a-2) x-a2+a.

(4) x2-p2q2+2pq-1.

(5) 2x2-ax-3a2.

(6) 3x2+10ax+3a2.

(7) pqx2+(q2−p2)xy—pqy2.

(8) (ab+cd) (c2+d2)+cd (a2+b2 — c2 — d2).
(9) 6x3-7x2-16x+12.

(10) (a+b+c) (ab+be+ac)-abc.

(11) x16+x8y+y16.

(12) x2-2ax-(1-a2).

CII.

GREATEST COMMON MEASURE AND
LEAST COMMON MULTIPLE.

1. Find the G.C.M. of—

(1) 6x2+x-35 and 10x2+21x-10.
(2) 2x-12x3+192:2-6x+9

and 4x3-18x2+19x−3.

(3) a2-12a+32 and a2-10a +16.

(4) 2x3-3x2y-xy2+6y3 and 2x3 — x2y+xy2 — 6y3. (5) 21x3-15x2 – 14x+ 10 and 21x3 +27x2 – 14x-18

(6) x5—4x3+3x and 2xa — 5x2 — 3.

(7) 3x3-3x-18 and 2x2+2x-12.

K

2. Find the L.C.M. of

(1) -3x3y3z, -12x2yz3, and 42x3yz3.
(2) x2-3x-70 and x3-39x+70.

(3) 3x3-2x2. x and 6x2-x-1.

(4) a3-4a2b+9ab2-10b3,

and a3+2a2b-3ab2+20b3

(5) x+2x2y-xy3-2y3 and a3—-2x2y—xy2+2y3.
(6) 2x-4, 4x2-1, and 4x2+1.

(7) x-1, x-2, 2-4, and x+1.
(8) a3-x3, a2-x2, and a3+203.

(9) x3-3x2+3x-1 and x3-x2-x+1.
(10)

-2x+2x-1 and x-2x3+2x2-2x+1.

(11) x2-(a-3)x-3a, x2-(a+2)x+2a,
and x2+(a-1)x-a.

(12) 2x2+xy-3y2, 2x2 — xy-3y2, x2 — 1,
and 422-9y2.

(15) 6x3+9x2y-4xy2 — 6y3°

a2+(2ac-b2)x2+c2x2

(16) a2+2abx+(2ac+b2) x2+2bcx3+· c2x4

(17)

a2+(ac-b2)x2+bcx3
a2+(ac—b2)x2 — bcx3

y3 (2a+b)y2+(2ab+a2)y-a2b
3y2-(4a+2b)y+2ab+a2

1

a2x2+a2 (3)

1

x2-(a+b)x+ab x2+(a−b)x−ab

1

(4) abx+a(a−b) (x−a)−b (a−b) (x−b)

a(b+c)

b(a+c)

c(a+b)

(18)

(a—b)(c—a)+(a−b)(b−c)+(c—a)(b−c)

(19)

(1−xy)(1+xy)—(x−y)(x+y) ̧
(1+xy)2+(x−y)2

a2-bc

b2-ca

c2-ab

(20) (a+b)(a+c)+(b+a)(b+c)+(c+a)(c+b)*

a2

b2

(22) (b−c)(c—a)+(c—a)(a−b)†

c+ a

(c-a)(a—b)+(a—b)(b—c)

c2

(23) (a−b)(a−c)+(b−a)(b−c)+(c—a)(c—b)*

1

1

1

(24) a(a−b)(a−c)+b(b−a)(b−c)+c(c—a)(c—b}