Good step by step explanations please!

The following is a statement and proof of the Binomial Theorem. Theorem: Let n be a positive integer and let a, b E C. Then ( at b ) " = > ( ? ) an b = a" + na"-16 + ( 32 ) an- 262 + ... + ( ? )an-ro" + ... + (", Jaba-1+ Be . Proof: 1. Consider (a + b)" = (a + b) (a + b) . .. (a + b). 2. When the brackets are multiplied out to get a term of the form a" "b", we choose b from r r brackets 3. and the a from n-r n - r brackets. Therefore the number of instances of a" "b" when we multiply out is equal to the number of ways of choosing r brackets from n. 5. In other words the coefficient of a" "b" is binomial(n,r) (" ) 6. The theorem follows. a. Fill in the gaps of the proof. b. In which step of the proof do we first use the definition of the binomial coefficient? 4 Your last answer was interpreted as follows: c. Step 6. finishes the proof because 0