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28.

[-2+ z2 *+- y+) x3 + 3x2y + 3xy? +33 +23 (x2 + 2xy + y2 — x 2 + xy +022

-227- 2xyz- y% 2.coy+3.cy

-Q? – xyz-xz 2x2y + 2xy2 + 2xyz

-wyz-y?z+xz2 ayo+y3-22 -ayz-y:z-yz? ayo+y+yz

xz? +yz? — 23

xz2+yza -- 23 1. 2-4-2+y 2. a4- 2a2b2 +64 +4abc-c4--a?+ 2ab +62-c? 3. af-2a2 +64 +4abc-c4-a-2ab +2° +2 4. Q4 + 86-(ap-2) +1674,4 --' +45 +46°2? 5. q*+86%2° (a-2) +1664x4--a?-4bx+46.2 6. 12x3–172y+3.cy® +2y3 - 3x-2y 7. 12.23 — 17a2y + 3xy2 +243 --4x2 – 3xy-y2 3. 205 + 151.2-264 ; 23 + 4x2 + 5x – 24 9. 25 +1512—264:22—4x +11 10. 1-2.0 - 31.2 + 7223 -30~4:1+40-10.0% 11. 1-20-31.2 + 72.33 — 3024--1-6x + 3.2 12. 24–2x+1=2+2-1 13. 204–2x+1--2-81 14. 64-96--223 +42° +80+16 15. 624-96: 3x 6

FACTORS.

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

1. a' + 2ab + b = (a+b) (a+b).
2. a - 2ab+b% = (a-b) (a-b).

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3. 22 +3ay +2y2 = (x+y) (x+2y).
4. 23 + xy + xy + y = (a +y) ( +y).
5. 24-y' = (2+ y) (x - y) (i+y)
6. 3.08 – 8.2%y - 3cy2 = (a2-3.cy) (3x +y).

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GREATEST COMMON MEASURE.

Proceed as in Arithmetic, or split up into factors.

1. 3x2y2 + 6x2y3 = 3x42 (x + 2xy) and 12xy + Scou? = 3xy" (4+ 3x) = 3.cy.

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3x2 + 3x Taking out factor 3x= x+1) 23 +1 (-2+1

203 + 2?

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6. 8.0-8

(2.x—2) 4 6.02-18x+12 = (2-2) (3x-6)

21—2

(32–6))=3

7. 8 +813 and 12a-24ab- 3662 4 (2a3 +263)

4 (30” — 6ab-962) 3a-6b-96) 12a3+1263 (4a +8b

12a3-24a2b-36ab?

24a21 + 36ab2 +1263
24-5-48ab-7263

2162) 84al? +8463 Multiplying last

3a-96 divisor by 4 4a + 4b) 120—24ab- 3662 (

12a2 + 12ab

- 36ab- 3662 -- 36ab-- 3662

8. 4a'ya-8127 and 2aya (2a-47)

12ay + ba+y 2a*yo (6ay +3a'y

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24 + 23

2003 + na 223 +2:2

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10. 203 +22-9c-9) 23 – 522 +2.x+12 (1 23+ 2— 9x – 9

(-1-17 -6° +112+21) 6x} +6.02 - 54.0-54

6x3-11-212 11) lla-33

1722 -330-54 2-3) – 62 +11x+21 (-63-7 ) (-62—7

6 -6x2 + 18x

102x2-198x— 324 70+ 21

102.02-187x - 357 -72 +21

11.
23 – 4.«— 252 +28=(x-7)(x2+3.2 — 4)


and x-14x2+49 (x-7)(x-7)

} =Q-7

12. x2 + 10x2 + 25x-28 (x+7) (22+3x+4) and x2 +14c+49 (+7) (x+7)

=x +7 14.0 x 13. 23-9x2 +15x (2-2) (22 — 7x+1)2 -2 & 2-4 (2-2) (x+2)

=x--2 x2

14. a +40-5, a +7a

(a+5) (a-1) ) =a? +4« — 5

(a +5) (a+2) =a” + 70-10 +10 and a-5

(a+5) (a-5) | =a?— 25

15. Q3 +1 and 23+ (a+1) (a?–a+1)

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

(a-2) (a-1) 2 and a2-4a +4

= (a—2) (a+1)

(a-2) (a-2)

17. b+by-yo-y3 and b+by-yo-y:=(y+1) (b-yo)

12 +by+62 +63 b+by+ya+y=(y+1) (b+y)

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18. a-a-2 (a+1) (a-2) and 1+ a

=a+1 (6+1) (a? +x+1) 19.3+42-4 and (3-2) (a +2) 2

= 2a--2 Buo+a-2 (31-2) (a +1) S

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SIMPLE EQUATIONS.

Having explained the four simple rules in Algebra, we will now proceed to Simple Equations in which these may

be worked out. An Equation is an expression in Algebra consisting of two portions united by the sign =, such that the quantity on the one side is the same in numerical value as the other, as a+b=7.

If this equation contain an unknown in the 1st power, that is not the square, cube, &c., it is called a Simple Equation, as ata=17.

As the two halves of the equality, united by =, are equal, the equality will not be destroyed by adding, subtracting, multiplying, or dividing, provided do the

to both sides of the equation. Thus if x + a= 7, then x + a + 3=7+3, and ax + 3 = 7–3, and 4 (x + a) = 4 x 7 or X + 1 7

4 4

we

same

2

1. x+6=5x— 3.2 x+6=2x

a=6

2. dx-c=a

dx=ato

ato
d

2 =

3. x+c=24+c x=24 4. 2x + a=6

2x + x = 6

3x=6

x=2

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