Question

Pra amanhã Gente me ajudem
Calcule:
a) ( a+b)5=a5+5a4b+10a3b2+10a2b3+5ab4+b5

Answer 1

(a + b)⁵ = a⁵ + 5a⁴b + 10a³b² + 10a²b³ + 5ab⁴ + b⁵

Passo a passo:

= (a + b)².(a + b)².(a + b)

= (a² + 2ab + b²).(a² + 2ab + b²).(a + b)

= (a².a²+a².2ab+a².b²+2ab.a²+2ab.2ab + 2ab.b² +b².a²+b².2ab + b².b²).(a + b)

= (a⁴ + 2a³b + a²b² + 2a³b+ 4a²b² + 2ab³ + a²b² + 2ab³ + b⁴).(a + b)

= (a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴).(a + b)

= a⁴.a + a⁴.b + 4a³b.a + 4a³b.b + 6a²b².a + 6a²b².b + 4ab³.a + 4ab³.b + b⁴.a + b⁴.b)

= a⁵ + a⁴b + 4a⁴b + 4a³b² + 6a³b² + 6a²b³ + 4a²b³ + 4ab⁴ + ab⁴ + b⁵

= a⁵ + 5a⁴b + 5ab⁴ + 10a³b² + 10a²b³ + 5ab⁴ + b⁵