Question

Which statement about the simplified binomial expansion of (a + b)", where n is a positive integer, is true?

Answer 1

A on edg, "The exponent of B will always be even"

Answer 2

`(a+b)^n  ={n \choose 0}a^((n))b^((0)) + {n \choose 1}a^((n-1))b^((1)) + {n \choose 2}a^((n-2))b^((2)) + .....  +{n \choose n}a^((0))b^((n))`

Explanation:

The Given question is INCOMPLETE as the statements are not provided.

Now, let us try and solve the given expression here:

The given expression is:
`(a +b)^n, n > 0`

Now, the BINOMIAL EXPANSION is the expansion which describes the algebraic expansion of powers of a binomial.

Here,
`(a+b)^n  = \sum_(k=0)^(n){n \choose k}a^((n-k))b^((k))`

or, on simplification, the terms of the expansion are:

`(a+b)^n  ={n \choose 0}a^((n))b^((0)) + {n \choose 1}a^((n-1))b^((1)) + {n \choose 2}a^((n-2))b^((2)) + .....  +{n \choose n}a^((0))b^((n))`

The above statement holds for each n > 0

Hence, the complete expansion for the given expression is given as above.