Question

Resolver esse binômio de Newton.
(a+b+c)3

Answer 1

Resposta: (a + b + c)³ = a³ + b³ + c³ + 3(a + b)(a + c)(b + c)

Explicação passo-a-passo:

(a + b + c)³ =

(a + b + c)²(a + b + c) =

(a² + b² + c² + 2ab + 2ac + 2bc)(a + b + c) =

a³ + a²b + a²c + ab² + b³ + b²c + ac² + bc² + c³ + 2a²b + 2ab² + 2abc + 2a²c + 2abc + 2ac² + 2abc + 2b²c + 2bc² =

a³ + b³ + c³ + 3a²b + 3a²c + 3b²c + 3bc² + 3ac² + 3ab² + 6abc =

a³ + b³ + c³ + 3(a²b + a²c + b²c + bc² + ac² + ab² + 2abc) =

a³ + b³ + c³ + 3[a²(b + c) + bc(b + c) + a(b² + c² + 2bc)] =

a³ + b³ + c³ + 3[(b + c)(a² + bc) + a(b + c)²] =

a³ + b³ + c³ + 3(b + c)[(a² + bc) + a(b + c)] =

a³ + b³ + c³ + 3(b + c)(a² + bc + ab + ac) =

a³ + b³ + c³ + 3(b + c)(a² + ab + bc + ac) =

a³ + b³ + c³ + 3(b + c)[a(a + b) + c(a + b)] =

a³ + b³ + c³ + 3(b + c)[(a + b)(a + c)] =

a³ + b³ + c³ + 3(a + b)(a + c)(b + c)

Abraços!