23.

a+b) a1+b1 (a3—a2b+ab2—b3+24

25.

26.

x+y-z) x2+2xy + y2-z2 (x+y+z
x2+ xy-xz

28.

[-yz+z2 x+y+ z) x2+3x2y+3xy2+y3+z3 (x2+2xy+y3− xz

x2 + x2y+x2z

2x2y+3xy2 — x2z
2x2y+2xy2+2xyz

xy2+y3 — x2z
xy2+y3 + y2z

2. at-2a2b2+b4+4abc2-c1÷a2+2ab+b2-c2
3. a4-2ab+b+4abc2-c4a2-2ab+b2+c2
4. a4+862x2 (a2-2)+16b4x4÷a2+4x+4b2x2
5. a1+8b2x2 (a2-2)+16b1x1÷a2-4bx+4b2x2
12-17 y+3xy2+2y3+3x-2y
7. 123-17y+3xy2+2y3÷4x2-3xy-y

6.

3.

9.

+151-264÷3+4x+5x-24
5+151-264÷x2-4x+11

10. 1-2x-31x2+72x3−30x1÷1+4x-10x2
11. 1-2x-31x2+72x3-30x1÷1−6x+3x2

12.

13. x-2x+1÷x-81

14.

6x4-96÷2x3+4x2+8x+16

15. 6x4-96÷3x-6

FACTORS.

This is the splitting up of a compound quantity

into simpler factors.

1. a2+2ab+b2 = (a+b) (a+b).
2. a2-2ab+b2 = (a−b) (a−b).
3. x2+3ay+2y2 = (x+y) (x+2y).
4. x2+x2y+xy2+y3 = (x2+y2) (x+y).
5. x-y+=(x2+ y2) (x−y) (x + y)
6. 3x3-8x3-3xу2 = (x2—3xy) (3x+y).

2

GREATEST COMMON MEASURE.

Proceed as in Arithmetic, or split up into factors. 1. 3x2y2 + 6x2y3 = 3xy2 (x + 2xy) and 12xy + 9x2y= 3xy (4+3x)

2.

=

×3+1) ×3+3x2+3x+1 (1

3xy?.

Taking out factor 3x= x+1) æ3 +1 (x2−x+1

7.

= (2x-2) 4

Ga2-18x+12= (2x−2) (3x−6)

8u3+863 and 12a2-24ab-36b2 4 (2a3 +2b3)

4 (3a2-6ab-962)

3a2-6ab-9b2) 12a3+12b3 (4a+8b

12a3-24a2b-36ab2

8. 4a3y2-8a2y3 and 2a2y2 (2a-4y) = 2a2y2 12a5y+6a1ys 2ay (6a3y+3a3y

9. (+) and 5-4-2 (x2+x)2== x2+2x+x3 Then 4+2+x2) x5-x-2

(x-3

— 3x4—6x3-3x2

3) 3x3+3.2

x2+x2) x1+2x3+x2 (x+1
x++ 23

+

10.

23+x-9x-9) x3-5x+2x+12 (1 x3+ x2-9x- 9

(-2-17

-62+11x+21) 6x+6x-54-54

6x-11a2-21x

23-42-25x+28_(a−7) (x2+3x-4)
and a-14+49-(x-7) (x-7)

x2+10x+252-28 and 22+14x+49

=

13.

=

=

12.

(x+7) (x2+3x+4) |
(x+7) (x+7)

(x+7) (23+ 3x + 4 ) }}

(x-2) (x2-7x+1)

-2 & x2-4(x-2) (x+2)

=x+7

=x--2

(a+5) (a-1)) =a2+4a-5
(a+5) (a+2)=a2 +7α-10
(a+5) (a−5)]=a2-25

15.

(a+1) (a-a+1)
(x+1) (a2+ab-a+1)

a2-3x+2, a2-a-
2 and a2-4a+4

b+by-y2-y3 and

(a-2) (a-1)

= (a−2) (a+1)
(a-2) (a-2))

17.

b+by—y2—y3=(y+1) (b−y3)

b2+by+b2+b 3 = b+by+ y2+ y2=(y+1) (b+ y2)