Question

Разложите на множители 12a^2b^2+6a^2b^3+12ab^3 b(b-2)^2+b^2(2-b) ax-5x-a^2+5a ab-ac+2c-2b-b+c

Answer 1

$12a^2b^2+6a^2b^3+12ab^3=6ab^2(2a+ab+2b) \\\\ b(b-2)^2+b^2(2-b)=b(b-2)^2-b^2(b-2)=b(b-2)(b-2-b)= \\\ =-2b(b-2) \\\\ ax-5x-a^2+5a=x(a-5)-a(a-5)=(a-5)(x-a) \\\\ ab-ac+2c-2b-b+c=ab-ac+3c-3b=a(b-c)-3(b-c)= \\\ =(b-c)(a-3)$