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23.

a+b) a1+b1 (a3—a2b+ab2—b3+24

a++a3b

a+b

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25.

26.

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

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x + y + z) x2+2xy+y2−z2 (x+y−z

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x+y+ z) x2+3x2y+3xy2+y3+z3 (x2+2xy+y2−xz x2+ x2y+x2z

2x2y+3xy2-x-z

-x-z-2xyz-y3z

-x2z- xyz-xz2

2x2y+2xy2+2xyz

-xyz-y2z+xz2

xy2+y3 — x2z

-xyz-y-z-yz2

xy2+y3 + y2z

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2. at-2a2b2+b2+4abc2-c1÷a2+2ab+b2-c2

3.

a1-2a2b2+b1+4abc2-c4÷a2—2ab+b2+c2

4. a*+862x2 (a2-2)+16b4x+÷a2+4bx+4b2x2 5. a⭑+862x2 (a2-2)+16b+x+÷a2-4bx+4b2x2

6.

12x3-1722y+3xy2+2y3÷3x-2y

7. 12x3-17x2y+3xy2+2y3÷4x2-3xy—y2 3. 25+151-264÷23+4x2+5x-24

9.

5151-264÷x2-4x+11

10. 1-2x-31x2+72x3-30x4÷1+4x-102 11. 1-2-3122+72x3-30a4÷1-6x+3x2 12. 4-2x+1÷x3+x2+x-1

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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).
x4-y+= (x2+y2) (x−y) (x+y)
6. 33-8xy-3xy2 = (x2-3xy) (3x+y).

5.

2

GREATEST COMMON MEASURE.

Proceed as in Arithmetic, or split up into factors. 1. 3x2y2 + 6x2y3 = 3xy2 (x + 2xy) and 12xy2 + 9x2y2 = 3xy2 (4+3x) = 3xy3.

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

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7.

(2x-2) 4

}

Ga2-18x+12= (2x-2) (3x-6) j

=2x-2

8a3+863 and 12a2-24ab-3662 4 (2a3+2b3) 4 (3a2-6ab-962)

3a2-6ab-9b2) 12a+1263 (4a+8b

12a3-24a2b-36ab2

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8. 4a3y2-8a2y3 and 2a2y2 (2a-4y)

12α3y3+6a1y3 2ay (6a3y +3a3y

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9. (2+) and a5-a4-23 (x2+x)2=x1+2x3+x3 Then x+2x3+x2) x5 — x1—2x3 (x−3

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10.

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

(-2-17

-6a2+11x+21) 6x+6x2-54-54

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x3-4x2-25x+28_ (x−7) (x2+3x−4)
and a-14+49-(x-7) (x-7)

=

12.

}

} = x

[ocr errors]

=x--2

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

=

13. 3-9x2+15x (x−2) (x2 −7x+1)

2 & x2-4

[blocks in formation]

=

(x-2) (x+2)

14.

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

15.

(a+1) (a2-a+1)
(x+1) (a2+ab—a+1)

a2+4a-5, a2+7a +10 and a2-5=

a3+1 and a3 +

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(a-2) (a-1))
(a−2) (a+1)
(a-2) (a-2))

b+by—y2—y3=(y+1) (b−y2)

2

b2+by+b2+b3 b+by+ y2+ y2=(y+1) (b+ y2)

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