Question

Desenvolva usando binômios de Newton

(2y-1)^5

Answer 1

Desenvolvendo ... 


(2y-1)^5 


= C5,0.[(2y)^(5-0).(-1)^0] + C5,1.[(2y)^(5-1).(-1)^1] + C5,2.[(2y)^(5-2).(-1)^2] + C5,3.[(2y)^(5-3).(-1)^3] + C5,4.[(2y)^(5-4).(-1)^4] + C5,5.[(2y)^(5-5).(-1)^5] 


= 1.[(2y)^5.1] + 5.[(2y)^4.-1] +  10.[(2y)^3.1] + 10.[(2y)^2.-1] + 5.[(2y)^1.1] + 1.[(2y)^0.-1]



= 32y^5 + 5.[-16y^4] + 10.[8y^3] + 10.[-4y^2] + 5.[2y] + 1.[-1] 


= 32y^5 - 80y^4 + 80y^3 - 40y^2 + 10y - 1   <----- Resposta                     ok

Answer 2

(2y-1)^5 

(2y)^5 + 5.(2y)^4.(1)^1 + 10.(2y)^3.(1)^2 + 10.(2y)^2.(1)^3 + 5.(2y)^1.(1)^4 + y^5. 

32y^5 + 5.(16y^4).(1) + 10.(8y^3).(1) + 10.(4y^2).(1) + 5.2y.(1) + y^5. 

32y^5 + 80y^4 + 80y^3 + 40y^2 + 10y + y^5.