Question

Помогите пожалуйста,все задания❣️

Answer 1

$1.1) 64x^5z^2-49x^7=x^5(64z^2-49x^2)=x^4(8z-7x)(8z+7x)\\1.2) a^3+64c^3=(a+4c)(a^2-4ac+16c^2)\\1.3) 32y^5-1=(2y-1)(16y^4+8y^3+4y^2+2y+1)\\2) (-3b+2)^3=-27b^3+54b^2-36b+8\\3) b(b-3)(b+3)-(b-1)(b^2+b+1)=b(b^2-9)-(b^3-1)=1-9b\\4.1) 81c^2-d^2+9c+d=(9c-d)(9c+d)+(9c+d)=(9c+d)(9c-d+1)\\4.2) 25-m^2-12mn-36n^2=25-(m+6n)^2=(25-m-6n)(25+m+6n)\\4.3) (x+2)^3-125=(x+2-5)((x+2)^2+5(x+2)+25)=(x-3)(x^2+9x39)$

$5.1) 121x^3-22x^2+x=0\\x(11x-1)^2=0\\x \in \{0,\frac{1}{11}\}\\\\5.2) x^3-2x^2-9x+18=0\\x^2(x-2)-9(x-2)=0\\(x^2-9)(x-2)=0\\(x-3)(x+3)(x-2)=0\\x\in\{-3,2,3\}\\\\5.3) x^3-6x^2+12x-9=0\\(x-3)(x^2-3x+3)=0\\x^2-3x+3=0: D=9-12<0\\x=3$

$6) 7^n+13^n-2=(7^n-1)+(13^n-1)=6(7^{n-1}+7^{n-2}+...+1)+12(13^{n-1}+13^{n-2}+...+1)$ кратно 6

$7) y^3+3y^2z+3yz^2+2z^3=y^2(y+2z)+yz(y+2z)+z^2(y+2z)=(y+2z)(y^2+yz+z^2)$