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

Step 1. Given Information

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

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

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In the following exercises, expand each binomial.(m+n)5

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Discrete Mathematics

Calculus

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

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