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, $^{10}C_5a^{5}b^{5}$