Преобразуйте выражение в многочлен: 1n+6)2; 2. (13h+1)2; 3. (4-3y)2; 4. (2k-8)2; 5. (3c+7d)2; 6.(9a+t)2; 7. (k-8)2; 8. (5-7m)2; 9. (13p-3)2; 10.(2f-10a)2; 11. (-3h+7)2; -y)2; 13.(с-10)2; 14. (11х+4)2; 15. (6+2y)2; 16. (4k-3)2; 17. (3c+2d)2; 18.(8х-3у)2; 19. (3а-5в)2; 20. (7с-2m)2; 21.(в+8)2; 22. (12h+2)2; 23. (5-2y)2; 24. (3k-4)2; 25. (2c+5d)2; 26.(8a+2t)2; 27. (3k-8а)2; 28. (5с-7m)2

1) (n+6)2 = 2n + 12 2) (13h + 1)2 = 26h + 2 3) (4-3y)2 = 8- 6y 4) (2k-8)2 = 4k -16 5) (3c + 7d)2 = 6c + 14d 6) (9а+t)2 = 18a + 2t

1) а²-3а+2/а²-5а+6=(a-2)(a-1)/(a-3)(a-2)=a-1/a-3
а²-3а+2=0
D=9-8=1, D>0
a₁=3+1/2=2, a₂=3-1/2=1
a²-5a+6=0
D=25-24=1, D>0
a₃=5+1/2=3, a₄=5-1/2=2
ответ: а-1/а-3
2)5а²-9а-2/а²-3а+2=(a-2)(a+0,2)/(a-2)(a-1)=a+0,2/a-1
5а²-9а-2=0
D=81+40=121, D>0
a₁=9+11/10=2, a₂=9-11/10=-0,2
a²-3a+2=0
D=9-8=1, D>0
a₃=3+1/2=2, a₄=3-1/2=1
ответ: а+0,2/а-1
3) 6х²+х-2/3х²-4х-4=(х-1/2)(х+2/3)/(х-2)(х+2/3)=х-1/2/х-2
6х²+х-2=0
D=1+48=49, D>0
x₁=-1+7/12=1/2
x₂=-1-7/12=-8/12=-2/3
3x²-4x-4=0
D=16+48=64, D>0
x₃=4+8/6=2, x₄=4-8/6=-4/6=-2/3
ответ: х-1/2/х-2

1)12a²b³+3a³b²+16b²-a²=3a²b²(4b+a) + (4²b² - a²)=3a²b²(4b+a)+(4b-a)(4b+a)=
   
= (4b+a)(3a²b² + 4b- a)

2) 49c² -14c+1 -21ac+3a =  (49c²-14c+1) -3a(7c - 1) = (7c - 1)²  - 3a(7c - 1) =

=(7c-1)(7c - 1 - 3a)

3)ax²+ay²+x^4+2x²y²+y^4 = a(x²+y²)+(x^4+2x²y²+y^4) = a(x²+y²) +(x²+y²)²=

   = (x²+y²) (a +x²+y²)

4)  27c³-d³+9c²+3cd+d² = [(3c)³-d³]+ (9c²+3cd+d²) =

=[(3c - d)(9c²+3cd+d²)] + (9c²+3cd+d²) = (9c²+3cd+d²) (3c-d+1)

5) b³-2b²-2b+1 =(b³ + 1) - 2b( b+1) = (b+1)(b² -b+1) - 2b(b+1) =

  = (b+1)(b² -b+1-2b) = (b+1)(b² -3b+1)