Mr. Rothman is using the Binomial Theorem to find the binomial expansion of (a+b)^7 Which of the following is a term in the expansion?(1 point)

Question

a. 21a^6b
b. a^4b^3
c. 21a^2b^5
d. 21a^2b^4

Answer 1

To find the term in the binomial expansion, we use the formula:

Term = (n choose k) * a^(n-k) * b^k

Here, n is the exponent of (a+b) (which is 7), k is the index of the term we want to find (starting from 0), a is the coefficient of a in the term, and b is the coefficient of b in the term.

Let's go through each option:

a. 21a^6b
Here, a^6 is the term raised to the 6th power, which is not present in the expansion. So, this is not a term in the expansion.

b. a^4b^3
Here, (n choose k) = (7 choose 3) = 35, a^(n-k) = a^(7-3) = a^4, and b^k = b^3. So, this is a valid term in the expansion.

c. 21a^2b^5
Here, a^2 is the term raised to the 2nd power, which is not present in the expansion. So, this is not a term in the expansion.

d. 21a^2b^4
Here, a^2 is the term raised to the 2nd power, which is not present in the expansion. So, this is not a term in the expansion.

Therefore, the answer is b. a^4b^3.