25.

26.

x+y−z) x2+2xy+y2−z2 (x+y+z

x2+ xy-xz

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

27. 1+2) 1-1624 (1-2x+4x-8x3

28.

[-yz+z2

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

2. a4-2a2b2+b4+4abc2-c1÷a2+2ab+b2-c2 3. a4-2a2b2+b4+4abc2-c4a2-2ab+b2+c2 4. a*+8b2x2 (a2-2)+16b4x4÷a2+4bx+4b2x2 5. a4+862x2 (a2-2)+16b11÷÷a2-4bx+4b2x2 6. 123-17x2y+3xy2+2y3÷3x-2y

7. 12x3-17x2y+3xy2+2y3÷4x2—3xy—y2

3.

9.

5+151-264÷23+4x2+5x-24 x5+151x-264÷x2-4x+11

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

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

2

3. x2+3ay+2y2 = (x+y) (x+2y).
4. x3 + x2y+xy2+y3 = (x2+y2) (x+y).
5. x1—y1 = (x2+ y2) (x−y) (x+y)

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

GREATEST COMMON MEASure.

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

2.

=

3xy2.

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

x3 + x2

18.

3a3-4a2)15a+at+2a3-36a2(5a2+7a+10+

19.

20.

15a5-20a4

21a4+2a3 21a+-28a3

4u2 3a-4a2

30a3-36a2

30a3-40a2

4a3

a+b) a5+b5 (a1-a3b+a2b2-ab3+b1

22.

-b2

a3+2a2+4a+8) 3a+-48 (3a-6

3a4+6a3+12a2+24a

-6a3-12a2-24a-48

-6a3-12a2-24a-48

25.

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

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