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.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.