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23.

214 a+b) a* +64 (a3-aob +ab-13+ attab

atb

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26.

x+y+z) x2 + 2xy + y2 – 22 (a +y->

2 + xy +

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27.

1+2x) 1-16x* (1-2x +4.x2 – 8.23
1+ 2.

4.29-1624
-2x-1624 4.2? + 8.2003
422

-8.63 – 16x4
-8.25-16x+

2.0 —

28.

(-42+z3 20+ y + x) x3 + 3x2y +3xy? +43 +33 (x2 +2.cy + y2 — xz + 7+com

-~~z—2xyz-y22 2x y + 3xy- -?

:- xyz-222 2x2y + 2xy2 + 2xyz

-yz-y?z+xz? xy2 +y3 – ?

-xyz-y-z-yza acy + y + yox

Qz+yz-73

azo+yz-23 1. 2*-:+y 2. af-2a-b2+14+4abc-ct--a + 2ab +62-22 3. q+-2ab2 +64 +4abc-c4-a-2ab +12+2 4. a4 + 862-2 (a?—2)+1664,+ --a+45x+46202 5. a* +86%2% (a-2) +166474--a—45x+4222 6. 1223 – 17x2y+3.cy® +2y3 -- 3x-2y 7. 12.23—17x*y + 3xy2 +2y3 --4«*— 3xy-ya 3. 25+1510-264-23 +4 + 5x - 24 9. 25 +151x—264--22—4x +11 10. 1-2x – 31x2 + 72x3 — 30x4:1+42-10.x2 11. 1-2.x-312° +72.3 - 30.04:1-6x + 3% 12. 24–2x+1:23 +22+x-1 13. 24-2.x+1=-x-81 14. 6x4-96; 2003 +422 +8x+16 15. 6.24-96:- 3x – 6

FACTORS.

This is the splitting up of a compound quantity into simpler factors.

1. a? + 2ab +12= (a+b) (a+b).
2. a-2ab + b2 = (a-b) (ab).
3. 2? + 3ay+2y2 = (a +y) (@+2y).
4. 23+x'j + xy + y = (x + y ) (c+y).
5. 2-y* = (x + y^) (x-y) (+y)
6. 3.03 - 8x®y - 3xy? = (2-3xy) (3x +y).

GREATEST COMMON MEASURE.

Proceed as in Arithmetic, or split up into factors.

1. 3.cy2 + 6.22y3 = 3xy” (x + 2xy) and 12.cy” + 9xy 3xyo (4+32) = 3.ey.

2.

23 +1) 3:3 + 3x + 3.2 +1 (1

23

+1

3.2 + 3x Taking out factor 3x= x+1) x3 +1 (22—<+1

23 + ?

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6. 8.0-8

(2x—2
60?–18x+12 = (2x-2) (3x-6)

*)}=_

= 21-2

7. 843 +863 and 12a-24ab- 3662 4 (2a3 +263)

4 (322—6ab-962) 3a2-6ab-9b%) 12a +1263 (4a +85

1293–24a2b-36ab?

24a2b + 36ab2 +1263
24rb48ab2-7263

2162) 84a0°+8493 Multiplying last

30–96 divisor by 4 42+46) 12a-24nb-366 (

12a” +12ab

- 36ab- 3662 -- 36ab- 3662

8. 4ay-812y3 and 2a’y (2a-4y)

12a73 + 6a+y: 2a®y (6ay + 3ay

= 2a ya

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20++ 2003

wil + m2 2003 + 22

10.

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203 +/- 9x-923 - 5.02 +2.4+12 (1
203 + 20 ? — 9x— 9

(-2-17
-622 +11%+21) 6x} +622—54.0-54

6x-11x2-21x
11) ll«-33

172-33x— 54
2-3) -6° +11x+21 (-63-7

6
-63+ 18.0

102x2–198x— 324
-7x+21

102.02-187x— 357
-7x+21

11.
23 -4° -25.2 +28 _ (1-7) (22 + 32-4)
and 2-14x +49 (x-7)(x-7)

=*-7

12.
22 + 10m2 + 25x— 28
and 22 +140+49

) )
13. 23—9.02 + 15x (x-2) (22— 7x+1)
-2 & 2-4 (2-2) (x+2)

=x--2

14.
a+4a-5, a +7a

(a +5) (a-1) ) =a +4u-5
+10 and a-5

= (a +5) (a+2) =a +7a-10
(a+5) (a-5) =a'-25

15.
3+1 and + (a+1) (a'-a+1)

=a+1
ba2 + ab +1 (2+1) (a +ab-a+1)
16.
a?- 3x+2, a-a-

(a-2) (a-1))
2 and a?-4a +4

(a-2) (a+1) =a-2

(a-2) (a-2)

17.
b+by-yo-y and b+by-yo-y=(y+1) (b-y)

72 +by+62 +63 + 6+by+ya +yo=(y+1) (6+ya)

4)}=
(2+3 (2+3x +4) }=x +7

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