Chapter 12: Q. 194E (page 1213)

In the following exercises, expand each binomial using Pascal's Triangle.
$(m + n)^{10}$

Short Answer

Expert verified

The expansion is $m^{10} + 10 m^{9} n + 45 m^{8} n^{2} + 120 m^{7} n^{3} + 210 m^{6} n^{4} + 252 m^{5} n^{5} + 210 m^{4} n^{6} + 120 m^{3} n^{7} + 45 m^{2} n^{8} + 10 m n^{9} + n^{10}$

Step by step solution

Given Information

Expand binomial using Pascal's Triangle

$(m + n)^{10}$

Solution

We have

The exponent is 10 hence eleventh row need to be considered

The expansion is

$\begin{array}{rcl} (m + n)^{10} & = & 1 m^{10} + 10 m^{9} n + 45 m^{8} n^{2} + 120 m^{7} n^{3} + 210 m^{6} n^{4} + 252 m^{5} n^{5} + 210 m^{4} n^{6} + 120 m^{3} n^{7} + 45 m^{2} n^{8} + 10 m n^{9} + 1 n^{10} \\ = & m^{10} + 10 m^{9} n + 45 m^{8} n^{2} + 120 m^{7} n^{3} + 210 m^{6} n^{4} + 252 m^{5} n^{5} + 210 m^{4} n^{6} + 120 m^{3} n^{7} + 45 m^{2} n^{8} + 10 m n^{9} + n^{10} \end{array}$

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In the following exercises, expand each binomial using Pascal's Triangle.
$(m + n)^{10}$

Short Answer

Step by step solution

Given Information

Solution

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In the following exercises, expand each binomial using Pascal's Triangle.(m+n)10

Short Answer

Step by step solution

Given Information

Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, expand each binomial using Pascal's Triangle.
$(m + n)^{10}$