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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 206E (page 1213)

In the following exercises, expand each binomial using Pascal's Triangle.
$(3 x - 4)^{4}$

Short Answer

Expert verified

Expansion is $81 x^{4} - 432 x^{3} + 288 x^{2} - 768 x + 256$

Step by step solution

Given Information

Expand binomial using Pascal's Triangle.

$(3 x - 4)^{4}$

Solution

We have

Here the exponent is 4 hence we need to consider fifth row

The expansion is

$(3 x - 4)^{4} = 1 {(3 x)}^{4} + 4 {(3 x)}^{3} (- 4) + 6 {(3 x)}^{2} {(- 4)}^{2} + 4 路 3 x {(- 4)}^{3} + 1 {(- 4)}^{4} = 81 x^{4} - 432 x^{3} + 288 x^{2} - 768 x + 256$

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In the following exercises, expand each binomial using Pascal's Triangle.(3x-4)4

Short Answer

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Given Information

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In the following exercises, expand each binomial using Pascal's Triangle.
$(3 x - 4)^{4}$