Question

Determine o termo em x^4 no desenvolvimento de (3x+2)^8

Answer 1

Tk+1=(n,p).(a)^n-k.(b)^k


Tk+1=(n,p).(a)^n-k.(b)^k

Tk+1=(8,k).(3x)^8-k.(2)^k

Tk+1=(8,k).(2)^k.(3x)^8-k

x^8-k=x^4

8-k=4
-k=4-8

-k=-4

k=-4/-1

k=4

Tk+1=(8,4).(2)^4.(3x)^4

T5=8!/(8-4)!4!.16.(811).x^4

T5=8.7.6.5.4!/4!4!.1296x^4

T5=8.7.6.5/4!.(1296).x^4

T5=7.6.5/3.(1296).X^4

T5=7.2.5.(1296).x^4

T5=70.(1296).x^4

T5=90720.x^4


espero ter ajudado!

bom dia !