Which of the following statements regarding the expansion of

Which of the following statements regarding the expansion of (x + y)^n are correct? A For any term x^ay^b in the expansion, a + b = n. B For any term x^a y^b in the expansion, a - b = n. C. The coefficients of x^a y^b and x^b y^a are equal. D. The coefficients of x^n and y^n both equal 1.

Solution

for any expansion (x+y)^n

x^a y^b

always a+b = n

statement A is true

lets take an example

(3x-2)^5 = 5C0 (3x)^5 (-2)^0 + 5C1 (3x)^4 (-2)^1 + 5C2 (3x)^3 (-2)^2 + 5C3(3x)^2(-2)^3 + ...

if you add the exponents of 3x and -2 it will always be equal to 5

hence a+b = n