Question

What is the sixth term in the binomial expression (5y+3)^10

Answer 1

1.₁₀C₀(5y)^10-0(3)^0
2:₁₀C₁(5y)^10-1(3)¹
3. ₁₀C₂(5y)^10-2(3)²
4. ₁₀C₃(5y)^10-3(3)³
5. ₁₀C₄(5y)^10-4(3)^4
6: ₁₀C₅(5y)^10-5(3)^5 ⇒
the answer is ₁₀C₅(5y)^5(3)^5

Answer 2

Answer : The sixth term in the binomial expression is,
`^(10)C_5a^(5)b^(5)`

Step-by-step explanation :

The general formula to calculate the term of binomial expression is:

`T_(r+1)=^nC_ra^((n-r))b^r`

where,

(r+1) = number of term

As we are given the binomial expression :

`(5y+3)^(10)`

For sixth term :

a = 5y

b = 3

n = 10

As, r + 1 = 6

So, r = 6 - 1

r = 5

Now put all the given values in the above formula, we get:

`T_(r+1)=^nC_ra^((n-r))b^r`

`T_(5)=^(10)C_5a^(10-5)b^5`

`T_(5)=^(10)C_5a^(5)b^(5)`

Thus, the sixth term in the binomial expression is,
`^(10)C_5a^(5)b^(5)`