Question

The following list gives the coefficients for the binomial expansion of (x + y)10. What is the value of B?

1, 10, 45, 120, 210, 252, 210, B, 45, 10, 1

1
10
45
120

Answer 1

The coefficients for the binomial expansion $(a+b)^n$ are symmetric across the middle term.

For the binomial expansion $(x+y)^{10}$ you will get 10+1=11 coefficients. The 6th term is middle term. If the coeeficients are

1, 10, 45, 120, 210, 252, 210, B, 45, 10, 1,

then the 6th term is 252.

This means that

• 5th and 7th terms are the same;
• 4th and 8th terms are the same;
• 3rd and 9th terms are the same;
• 2nd and 10th terms are the same;
• 1st and 11th terms are the same.

If 4th and 8th terms are the same, then B=120.

Answer: correct choice is D

Answer 2

Answer: Answer choice is D

Step-by-step explanation: