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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 207E (page 1213)

In the following exercises, expand each binomial using Pascal's Triangle.
$(3 x - 5)^{3}$

Short Answer

Expert verified

Expansion is $27 x^{3} - 135 x^{2} + 225 x - 125$

Step by step solution

01

Given Information

Expand binomial using Pascal's Triangle.

$(3 x - 5)^{3}$

02

Solution

We have

Here the exponent is 3 hence we need to consider fourth row

The expansion is

$(3 x - 5)^{3} = 1 (3 x)^{3} + 3 (3 x)^{2} (- 5) + 3 (3 x) (- 5)^{2} + 1 (- 5)^{3} = 27 x^{3} - 135 x^{2} + 225 x - 125$

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Most popular questions from this chapter

Find a general term for the sequence whose first five terms are shown. −3, 9, −27, 81, −243, ...

Write the first five terms of the sequence whose general term is $a_{n} = 2^{n} - 5$

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${\sum 6}_{i = 1}^{15} {(2)}^{i}$

In the following exercises, expand each binomial using Pascal's Triangle.

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