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Section 10.18 : Binomial Series

For problems 1 – 3 use the Binomial Theorem to expand the given function.

1. \(\displaystyle {\left( {\frac{1}{2} + \frac{2}{3}x} \right)^4}\)
2. \({\left( {1 - 8x} \right)^5}\)
3. \({\left( {3 + 7x} \right)^6}\)

For problems 4 – 6 write down the first four terms in the binomial series for the given function.

1. \({\left( {8 + 4x} \right)^{ - 4}}\)
2. \(\sqrt {16 + 25x} \)
3. \(\sqrt[4]{{16 - 4x}}\)