§. Natural va butun sonlar

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