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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 202E (page 1069)

In the following exercises, expand each binomial using Pascal's Triangle.
$(z - 2)^{6}$

Short Answer

Expert verified

Expansion is $z^{6} - 12 z^{5} + 60 z^{4} - 160 z^{3} + 240 z^{2} - 192 z + 64$

Step by step solution

01

Given Information

Expand binomial using Pascal's Triangle.

$(z - 2)^{6}$

02

Solution

We have

Here the exponent is 6 hence we need to consider seventh row

The expansion is

$(z - 2)^{6} = 1 z^{6} + 6 z^{5} (- 2) + 15 z^{4} {(- 2)}^{2} + 20 z^{3} {(- 2)}^{3} + 15 z^{2} {(- 2)}^{4} + 6 z {(- 2)}^{5} + 1 {(- 2)}^{6} = z^{6} - 12 z^{5} + 60 z^{4} - 160 z^{3} + 240 z^{2} - 192 z + 64$

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Most popular questions from this chapter

In the following exercises, simplify each expression using the properties for exponents.

$ⓐ q^{27} \cdot q^{15} ⓑ 5^{x} \cdot 5^{4 x} ⓒ 9 u^{41} \cdot 7 u^{53} ⓓ c^{5} \cdot c^{11} \cdot c^{2}$

Simplify:

$(a) \sqrt[3]{- 625} (b) \sqrt[4]{- 324} .$

In the following exercises, add the polynomials.

$(x^{2} + 6 x + 8) + (- 4 x^{2} + 11 x - 9)$

For the function $f (x) = 25 x^{2} - 81$ , find:
(a) the zeros of the function.

(b) the x-intercepts of the graph

of the function.
(c) the y-intercept of the graph of the

function.

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{1}{2} - \frac{4}{x^{2}} \leq \frac{1}{x}$

See all solutions

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