Question

Упростите выражение
(a-b)(a^2+ab+b^2)+b(a-b)^2-a(a-b)(a+2b)

Answer 1

(a-b)(a²+ab+b²)+b(a-b)²-a(a-b)(a+2b)=а³-b³+b(a²-2ab+b²)-a(a²+2ab-ab-2b²)=
a³-b³+a²b-2ab²+b³-a³-2a²b+a²b-2ab²=-2ab²

Answer 2

$(a-b)(a ^{2} +ab+b ^{2} )+b(a-b) ^{2} -a(a-b)(a+2b)= \ =a ^{3} -b ^{3} +b(a ^{2} +b ^{2} -2ab)-a(a ^{2} +2ab-ab-2b ^{2} )= \ =a ^{3} -b ^{3} +a ^{2} b+b ^{3} -2ab ^{2} -a(a ^{2} +ab-2b ^{2} )= \ =a ^{3} +a ^{2} b -2ab ^{2} -a ^{3} -a ^{2} b+2ab ^{2} =0$