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Which statement about the simplified binomial expansion of (a + b2)n, where n is a positive integer, is true?
A.The exponent of b will always be even.
B.The exponent of a will always be odd.
C.The sum of the exponents of a and b will always equal n.
D.The sum of the exponents of a and b will always equal n – 1.

Respuesta :

We are considering the expansion of the binomial [tex] ( a+b^{2} )^{n} [/tex]

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

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

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, 

[tex]( a+b^{2} ) ^{2}= a^{2}+2ab^{2}+ b^{4} [/tex]

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



Answer: Only A
Martebi

There are different kinds of binomial expansion. The true statement about the simplified binomial expansion is that the exponent of b will always be even.

Why do one use binomial expansion?

The binomial formula is a term used in statistics that is often employed in the counting and for calculating of the probabilities found in an experiments.

A  binomial series expansion, is one that is used in calculus for rewriting hard functions into a more kind of simpler or binomial form. There are 2 terms in binomial. The exponent of b will always be even as it is an even exponent that will always gives a positive result.

Learn more about binomial expansion from

https://brainly.com/question/13602562

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