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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 215E (page 1213)

In the following exercises, expand each binomial.
$(m + n)^{5}$

Short Answer

Expert verified

Expansion is $m^{5} + 5 m^{4} n + 10 m^{3} n^{2} + 10 m^{2} n^{3} + 5 m n^{4} + n^{5}$

Step by step solution

01

Step 1. Given Information

Expand $(m + n)^{5}$

02

Step 2. Solution

We have

$(m + n)^{5} = (\begin{array}{l} 5 \\ 0 \end{array}) m^{5 - 0} n^{5 - 5} + (\begin{array}{l} 5 \\ 1 \end{array}) m^{5 - 1} n^{5 - 4} + (\begin{array}{l} 5 \\ 2 \end{array}) m^{5 - 2} n^{5 - 3} + (\begin{array}{l} 5 \\ 3 \end{array}) m^{5 - 3} n^{5 - 2} + (\begin{array}{l} 5 \\ 4 \end{array}) m^{5 - 4} n^{5 - 1} + (\begin{array}{l} 5 \\ 5 \end{array}) m^{5 - 5} n^{5 - 0} = m^{5} + 5 m^{4} n + 10 m^{3} n^{2} + 10 m^{2} n^{3} + 5 m n^{4} + n^{5}$

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