Chapter 12: Q. 193E (page 1213)

In the following exercises, expand each binomial using Pascal's Triangle.
$(a + b)^{8}$

Short Answer

Expert verified

Expansion is $a^{8} + 8 a^{7} b + 28 a^{6} b^{2} + 56 a^{5} b^{3} + 70 a^{4} b^{4} + 56 a^{3} b^{5} + 28 a^{2} b^{6} + 8 a b^{7} + b^{8}$

Step by step solution

Given Information

Expand binomial using Pascal's Triangle.

$(a + b)^{8}$

Solution

We have

Here the exponent is 8 hence we need to consider ninth row

The expansion is

$(a + b)^{8} = 1 a^{8} + 8 a^{7} b + 28 a^{6} b^{2} + 56 a^{5} b^{3} + 70 a^{4} b^{4} + 56 a^{3} b^{5} + 28 a^{2} b^{6} + 8 a b^{7} + 1 b^{8} = a^{8} + 8 a^{7} b + 28 a^{6} b^{2} + 56 a^{5} b^{3} + 70 a^{4} b^{4} + 56 a^{3} b^{5} + 28 a^{2} b^{6} + 8 a b^{7} + b^{8}$

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In the following exercises, expand each binomial using Pascal's Triangle.
$(a + b)^{8}$

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)8

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

Logic and Functions

Mechanics Maths

Probability and Statistics

Decision Maths

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, expand each binomial using Pascal's Triangle.
$(a + b)^{8}$