write the fifth term of (x + y)^5

[NEHA]

write the fifth term of (x + y)^5

(a+b)^n = nCk (a^(n-k) b^(k))
(a+b)^n > (x+y)^5

(x+y)^5 = 5C0(x^(5-0)y^0) < term one
(x+y)^5 = 5C1(x^(5-1)y^1) < term two
(x+y)^5 = 5C2(x^(5-2)y^2) < term three
(x+y)^5 = 5C3(x^(5-3)y^3) < term four
(x+y)^5 = 5C4(x^(5-4)y^4) < term five

so fifth term is : 5C4(x^(5-4)y^4)

 

[soroban]

Hello, NEHA!

What you did was correct, but . . .

Write the fifth term of \(\displaystyle (x\,+\,y)^5\)

\(\displaystyle (a\,+\,b)^n \:= \:_nC_ka^{n-k} b^k\)

\(\displaystyle (x\,+\,y)^5 \:= \:\left\{\begin{array}{ccccc}_5C_0x^{5-0}y^0 & \;\Leftarrow &\text{term one} \\ _5C_1x^{5-1}y^1 & \;\Leftarrow & \text{term two} \\_5C_2x^{5-2}y^2 & \;\Leftarrow & \;\text{term three} \\ _5C_3x^{5-3}y^3 & \;\Leftarrow & \text{term four} \\ _5C_4x^{5-4}y^4 & \;\Leftarrow & \text{term five}\end{array}\)



so fifth term is: \(\displaystyle _5C_4x^{5-4}y^4\;\;\) . . . Are you going to leave it like that?

Or will you write: \(\displaystyle \L\,5xy^4\)