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

Accepted Solution

Answer:[tex](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)}[/tex]Step-by-step 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: [tex](a +b)^n, n > 0[/tex]Now, the BINOMIAL EXPANSION is the expansion which  describes the algebraic expansion of powers of a binomial.Here, [tex](a+b)^n  = \sum_{k=0}^{n}{n \choose k}a^{(n-k)}b^{(k)}[/tex]or, on simplification, the terms of the expansion are:[tex](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)}[/tex]The above statement holds for each  n > 0Hence, the complete expansion for the given expression is given as above.