Question

How many coefficients are in (a+b)^3?
A) 1
B) 2
C) 3
D) 4

Answer 1

In the expansion of (a+b)^3, there are 4 coefficients, including those with an implicit coefficient of 1 for terms like a^3 and b^3.

Step-by-step explanation:

To determine how many coefficients are in the expansion of (a+b)^3, we need to apply the binomial theorem or expand it manually. When we expand (a+b)^3, we get:

a^3 + 3a^2b + 3ab^2 + b^3.

Each of these terms has a coefficient. The coefficients are 1 (implicit for a^3 and b^3), 3 (for 3a^2b), and 3 (for 3ab^2). Therefore, there are a total of 4 coefficients when we count all terms, including those with the implicit coefficient of 1.

So the answer is D) 4.