Question

Which statement about the simplified binomial expansion of (a + b2)n, where n is a positive integer, is true?

Answer 1

We are considering the expansion of the binomial $( a+b^{2} )^{n}$

since $( a+b^{2} )^{n} =( a+b^{2} )( a+b^{2} )...( a+b^{2} )$ n many times, the first term will be the multiplication of a n times with itself so $a^{n}$

and the last term will be the multiplication of $b^{2}$ n times with itself that is $(b^{2}) ^{n}= b^{2n}$

2n, the exponent of b, is even no matter what n is, so 

A) is true

B) is not true because if n is odd, the coefficient of a is odd

C) D)

consider the case n=2, 

$( a+b^{2} ) ^{2}= a^{2}+2ab^{2}+ b^{4}$

consider the term $2ab^{2}$, the sum of the exponents of a and be is neither n (2) , nor n-1 (1)



Answer: Only A

Answer 2

Answer:

It's A

Step-by-step explanation:

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