§. Natural va butun sonlar



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  1. Ko’phadlarni ko’paytuvchilarga ajrating.

1.1) x4+x2+1 1.2) x16-1 1.3) x8+x4+1 1.4) 2x4+x3+4x2+x+2 1.5) x4-12x3+47x2-60x 1.6) x5+x4+1 1.7) y2z2(y2-z2) + x2z2(z2-x2)+x2y2(x2-y2) 1.8) x(y2-z2)+y(z2-x2)+z(x2-y2) 1.9) (b-c)(b+c)2+(c-a)(c+a)2+(a-b)(a+b)2 1.10) a(b-c)3+b(c-a)3+c(a-b)3 1.11) x(y+z)(y2-z2) + y(z+x)(z2-x2)+z(y+x)(x2-y2) 1.12) x6+27 1.13) x4+3x2+4 1.14) (x+2)(x+3)(x+4)(x+5)-24 1.15) x4+4y4 1.16) 27x3-27x2+18x-4 1.17) (x+1)(x+3)(x+5)(x+7)+15 1.18) x3+y3+z3-3xyz 1.19) (x2+x+1)2 + 3x(x2+x+1)+2x2 1.20) x2y2-x2+4xy-y2+1 1.21) [a(x+y)+b(x-y)]2-[a(x-y)+b(x+y)]2 1.22) x6-y6+x4+x2y2+y4 1.23) 9x3+7x2-7x-9 1.24) 2x4+7x3-2x2-13x+6 1.25) x(x+1)(x+2)(x+3)+1 1.26) a4+b4+c4-2a2b2-2a2c2-2b2c2 1.27) (x2+x-1)(x2+3x-1)+x2 1.28) x4+5x2+9 1.29) (x+1)4 +2(x+1)3+x(x+2) 1.30) x3+9x2+11x-21 1.31) x2-3xy+2y2-2x+4y 1.32) x3+2y3-3xy2 1.33) (x+y)4 +x4+y4 1.34) x2y + xy2+x2z+xz2+y2z+yz2+2xyz 1.35) x5+x+1 1.36) x5+x4+1 1.37) a4(b-c) + b4(c-a)+c4(a-b) 1.38) (x-y)(y+z)(z+x)+(y-z)(z+x)(x+y)+(z-x)(x+y)(y+z) 1.39) x9 + 5x5+ x4+4x+4

2. Quyidagi darajalarni ko’phad shaklni aniqlang.



2.1) (x+2y)6 2.2) (x-2y)6 2.3) 2.4) 2.5) 2.6) 2.7) 2.8)

3. Berilgan binom yoyilmasida x qatnashmagan had koeffitsiyentini toping.

4. Agar binom yoyilmasida beshincha had x ga bog’liq bo’lmasa, n ning qiymatini aniqlang.

5. (1+x-3x2)2018 ifodada qavslarni ochib, o’xshash hadlari ixchamlagandan so’ng hosil bo’lgan ko’phadning koeffitsiyentlari yig’indisini toping.

6. (1+x-3x2)2018 ifodada qavslarni ochib, o’xshash hadlari ixchamlagandan so’ng hosil bo’lgan ko’phadning juft darajalari oldidagi koeffitsiyentlari yig’indisini aniqlang.

7. (1+x-3x2)2018 ifodada qavslarni ochib, o’xshash hadlari ixchamlagandan so’ng hosil bo’lgan ko’phadning toq darajalari oldidagi koeffitsiyentlari yig’indisini aniqlang.

8. (1+x)n +(1+x)n+1 yoyilmaning koeffitsiyentlari yig’indisi 1536 ga teng bo’lsa, x6 ning oldidagi koeffitsiyentini aniqlang.

9. (x+3)100 = a0+a1x +……+a100x100 shaklda bo’lsa, quyidagilarning qiymatini aniqlang.

9.1) a45 9.2) a0+a1 +……+a100 9.3) a0-a1+a2-a3+……+a100

2. Agar nol bo’lmagan a va b haqiqiy sonlar uchun ab=a-b shart o’rinli bo’lsa, ifodaning qiymatini toping.

A)-2 B) C) D)2

10. ni soddalashtiring



11. ni soddalashtiring

12. c ni soddalashtiring

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