23. a+b) a1+b1 (a3—a2b+ab2—b3+24 a++a3b a+b 25. 26. x+y-z) x2+2xy + y2-z2 (x+y+z x + y + z) x2+2xy+y2−z2 (x+y−z 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 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 This is the splitting up of a compound quantity into simpler factors. 1. a2+2ab+b2 = (a+b) (a+b). 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. Taking out factor 3x=x+1) 3+1 (x2-x+1 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 8. 4a3y2-8a2y3 and 2a2y2 (2a-4y) 12α3y3+6a1y3 2ay (6a3y +3a3y 9. (2+) and a5-a4-23 (x2+x)2=x1+2x3+x3 Then x+2x3+x2) x5 — x1—2x3 (x−3 10. 2+x-9x-9) x3-5x+2x+12 (1 x3+ x2-9x- 9 (-2-17 -6a2+11x+21) 6x+6x2-54-54 x3-4x2-25x+28_ (x−7) (x2+3x−4) = 12. } } = x =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 = (x-2) (x+2) 14. (a+5) (a-1)) =a2+4a-5 15. (a+1) (a2-a+1) a2+4a-5, a2+7a +10 and a2-5= a3+1 and a3 + (a-2) (a-1)) b+by—y2—y3=(y+1) (b−y2) 2 b2+by+b2+b3 b+by+ y2+ y2=(y+1) (b+ y2) |