Which of the following statements regarding the expansion of (x + y)^n are correct?
a. the coefficients of xn and y^n both equal 1.
b. for any term x^ay^b in the expansion, a + b = n.
c. for any term x^ay^b in the expansion, a - b = n.
d. the coefficients of x^ay^b and x^by^a are equal.

A, B and D are true statements.

Step-by-step explanation:

We are given a binomial expansion

Now we will check each option

Option A: The coefficients of and both equal 1.

If we see first and last term of the expansion, This statement is true.

Option B: For any term in the expansion, a + b = n.

Let we take 3rd term of expansion

Here, a=n-2 and b=2

If we do  a+b = n-2+2=n

a+b=n is true statement.

Option C: For any term x^ay^b in the expansion, a - b = n.

Let we take 3rd term of expansion

Here, a=n-2 and b=2

If we do  a-b = n-2-2=n-4≠n

a-b=n is false statement.

Option D: The coefficients of x^ay^b and x^by^a are equal.

If we take second term from beginning and last of the expansion.

This statement true.

The coefficients of xn and y^n both equal 1.

For any term x^ay^b in the expansion, a + b = n.

The coefficients of x^ay^b and x^by^a are equal.

Step-by-step explanation:

Ap ex

On my ap ex quiz it showed "x^n-1 and y^n-1 both equal 1" in this case that is not true.

goog may have it for you