Question

разложите на множители (a+b)^3-(a-b)^3
(2x+y)^3+(x-2y)^3
(2mn-1)^3+1
(3a-2b)3^3+8b^3

Answer 1

$1. \ (a+b)^3-(a-b)^3=(a+b-a+b)((a+b)^2+(a+b)(a-b)+(a-b)^2 \ =2b(a^2+2ab+b^2+a^2-b^2 +a^2-2ab+b^2)=2b(3a^2+b^2) \ 2. \ (2x+y)^3 +(x-2y)^3 = (2x+y+x-2y)((2x+y)^2-(2x+y)(x-2y) \ +(x-2y)^2)= (3x-y)(4x^2+4xy+y^2-2x^2+3xy+2y^2+x^2+4xy \ +4y^2) =(3x-y)(3x^2+11xy+7y^2) \ 3.(2mn-1)^3+1=(2mn-1+1)(2m^2n^2-4mn+1-2mn-1+1)= \ 2mn(2m^2n^2-6mn+1) \ (3a-2b)^3+8b^3=(3a-2b+2b)(9a^2-12ab+4b^2-6ab-4b^2+4b^2= \ 3a(9a^2-18ab+4b^2)$