Chapter 12: Q. 196E (page 1213)

In the following exercises, expand each binomial using Pascal's Triangle.
$(x - y)^{5}$

Short Answer

Expert verified

The expansion is $x^{5} - 5 x^{4} y + 10 x^{3} y^{2} - 10 x^{2} y^{3} + 5 x y^{4} - y^{5}$

Step by step solution

Given Information

Expand binomial using Pascal's Triangle.

$(x - y)^{5}$

Solution

We have

The exponent is 5 hence sixth row need to be considered

The expansion is

$(x - y)^{5} = 1 x^{5} + 5 x^{4} (- y) + 10 x^{3} {(- y)}^{2} + 10 x^{2} {(- y)}^{3} + 5 x {(- y)}^{4} + 1 {(- y)}^{5} = x^{5} - 5 x^{4} y + 10 x^{3} y^{2} - 10 x^{2} y^{3} + 5 x y^{4} - y^{5}$

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In the following exercises, expand each binomial using Pascal's Triangle.
$(x - y)^{5}$

Short Answer

Step by step solution

Given Information

Solution

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In the following exercises, expand each binomial using Pascal's Triangle.(x-y)5

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

Statistics

Mechanics Maths

Geometry

Discrete Mathematics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, expand each binomial using Pascal's Triangle.
$(x - y)^{5}$