Question

Разложите на множители (b-3)^3-1 и (a+b)^3-(a-b)^3

Answer 1

$(b-3)^3-1 = (b-3)^3-1^3 = (b-3 -1)((b-3)^2+(b-3)+1) = \\ = (b-4)(b^2-6b+9+b-2)=(b-4)(b^2-5b+7)$

$(a+b)^3-(a-b)^3 = (a+b - a+b)((a+b)^2 +(a+b)(a-b) + \\ +(a-b)^2)) = \\ =2b(a^2+2ab+b^2 +a^2 - b^2 + a^2-2ab+b^2)= \\ =2b(3a^2+b^2)$