Question

Each term in a binomial expansion has degree n; therefore, the product of the exponents of each term is n.

true
or
false

Answer 1

False. The SUM of the exponents of each term is n.

(a+b)^n = a^n b^0 + a^(n-1) b^1 + ......

Answer 2

False

Explanation:

In any binomial expansion of the form

`(x+a)^n = \Sigma_0^n nCr x^(n-r) a^(r)`

We find that each term has decreasing powers of x by 1 and increasing powers of a by 1, such that the sum of exponents is always n

Hence product of exponents of each term cannot be n.

The given statement is false.

Only the sum of the exponents of each term in a binomial expansion has degree n