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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 204E (page 1213)

In the following exercises, expand each binomial using Pascal's Triangle.
$(4 x - 1)^{3}$

Short Answer

Expert verified

Expansion is $64 x^{3} - 48 x^{2} + 12 x - 1$

Step by step solution

01

Given Information

Expand binomial using Pascal's Triangle.

$(4 x - 1)^{3}$

02

Solution

We have

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

The expansion is

$(4 x - 1)^{3} = 1 {(4 x)}^{3} + {3 (4 x)}^{2} (- 1) + 3 (4 x) {(- 1)}^{2} + (- 1) = 64 x^{3} - 48 x^{2} + 12 x - 1$

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Most popular questions from this chapter

In the following exercises, determine if each sequence is arithmetic, and if so, indicate the common difference.

$13, 9, 5, 1, - 3, - 7, . . . . .$

Write the first five terms of the sequence whose general term is $a_{n} = 3 n - 4$

Find the sum: $\sum_{i = 1}^{30} (6 i - 4)$

Determine if each sequence is geometric. If so indicate the common ratio.

ⓐ. $7, 21, 63, 189, 567, 1, 701, \dots$

ⓑ. $64, 16, 4, 1, 1 4, 1 16, \dots$

ⓒ. $2, 4, 12, 48, 240, 1, 440, \dots$

Write the first five terms of the sequence where the first term is $7$ and the common ratio is $r = - 3$ .

See all solutions

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