Question

2 Demonstrati identitatile.
a) (a+b)³=a³+3a²b+3ab²+b³, pentru orice a,b apartine R
b) (a-b)³=a³-3a²b+3ab²-b³ pentru orice a,b apartine R
c) a³+b³=(a+b)(a²-ab+b²) pentru orice a,b apartine R
d) a³-b³=(a-b)(a²+ab+b²) apartine orice a,b apartine R
Va rog rapid este lectia relatia de egalitate in multimea numerelor reale

Answer 1

a)(a+b)³=(a+b)²(a+b)=(a²+2ab+b²)(a+b)=a³+a²b+2a²b+2ab²+ab²+b³=
=a³+3a²b+3ab²+b³
b)(a-b)³=(a-b)²(a-b)=(a²-2ab+b²)(a-b)=a³-a²b-2a²b+2ab²+ab²-b³=
=a³-3a²b+3ab²-b³
c)(a+b)(a²-ab+b²)=a³-a²b+ab²+a²b-ab²+b³=a³+b³
d)(a-b)(a²+ab+b²)=a³+a²b+ab²-a²b-ab²-b³=a³-b³
pt. orice a,b∈R