Chapter 12: Q. 197E (page 1213)

In the following exercises, expand each binomial using Pascal's Triangle.
$(a - b)^{6}$

Short Answer

Expert verified

The expansion is $a^{6} - 6 a^{5} b + 15 a^{4} b^{2} - 20 a^{3} b^{3} + 15 a^{2} b^{4} - 6 a b^{5} + b^{6}$

Step by step solution

Given Information

Expand binomial using Pascal's Triangle.

$(a - b)^{6}$

Solution

We have

The exponent is 6 hence seventh row need to be considered

The expansion is

$(a - b)^{6} = 1 a^{6} + 6 a^{5} (- b) + 15 a^{4} {(- b)}^{2} + 20 a^{3} {(- b)}^{3} + 15 a^{2} {(- b)}^{4} + 6 a {(- b)}^{5} + 1 {(- b)}^{6} = a^{6} - 6 a^{5} b + 15 a^{4} b^{2} - 20 a^{3} b^{3} + 15 a^{2} b^{4} - 6 a b^{5} + b^{6}$

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In the following exercises, expand each binomial using Pascal's Triangle.
$(a - b)^{6}$

Short Answer

Step by step solution

Given Information

Solution

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In the following exercises, expand each binomial using Pascal's Triangle.(a-b)6

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

Geometry

Calculus

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Study anywhere. Anytime. Across all devices.

In the following exercises, expand each binomial using Pascal's Triangle.
$(a - b)^{6}$