Question

Помогите, даю 50баллов

Answer 1

$1); ; -3,5ab^3c^2cdot 1,6a^3bc=-5,6a^4b^4c^3\\(-2frac{3}{4})b^4c^2cdot (-frac{8}{33})b^2c^4=frac{11}{4}cdot frac{8}{33}b^6c^6=frac{2}{3}b^6c^6\\2); ; (x-1)(x-2)(x+3)-(x+1)(x+2)(x-3)=\\=(x^2-3x+2)(x+3)-(x^2+3x+2)(x-3)=\\=x^3+3x^2-3x^2-9x+2x+6-(x^3-3x^2+3x^2-9x+2x-6)=\\=6+6=12$

$3); ; (2b+a^3)(a^3-2b)=(a^3)^3-(2b)^2=a^9-4b^2\\(x^2+y^2)(x^4-x^2y^2+y^4)=(x^2)^3+(y^2)^3=x^6+y^6\\4); ; 16ab^3-20a^2b^2=4ab^2cdot (4b-5a)\\18x^4y^2-12x^5y^3=6x^4y^2cdot (3-2xy)\\mn-2m+4n-8=m(n-2)+4(n-2)=(n-2)(m+4)\\5); ; (x-1)(underbrace {x^7+x^6+x^5+x^4+x^3+x^2+x+1}_{geom.progr.; ,; b_1=1; ,; q=x})=\\=(x-1)cdot frac{1-b_{n}q}{1-q}=(x-1)cdot frac{1-x^7cdot x}{1-x}=-(1-x^8)=x^8-1; ;\\x^8-1=x^8-1$