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Chapter 8: Problem 38
Find each indicated sum. $$\sum_{i=3}^{7} 12$$
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Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ \left(2 x^{3}-1\right)^{4} $$
Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ \left(x^{2}+y\right)^{4} $$
Which one of the following is true? a. The binomial expansion for \((a+b)^{n}\) contains \(n\) terms. b. The Binomial Theorem can be written in condensed form as \((a+b)^{n}=\sum_{r=0}^{n}\left(\begin{array}{l}n \\ r\end{array}\right) a^{n-r} b^{r}\). c. The sum of the binomial coefficients in \((a+b)^{n}\) cannot be \(2^{n}\). d. There are no values of \(a\) and \(b\) such that \((a+b)^{4}=a^{4}+b^{4}\)
Describe the pattern on the exponents on \(b\) in the expansion of \((a+b)^{n}\).
Find the term indicated in each expansion. \((x+2 y)^{10} ;\) the term containing \(y^{6}\)
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