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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 199E (page 1069)

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

Short Answer

Expert verified

The expansion is $x^{3} + 15 x^{2} + 75 x + 125$

Step by step solution

01

Given Information

Expand binomial using Pascal's Triangle.

$(x + 5)^{3}$

02

Solution

We have

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

The expansion is

$(x + 5)^{3} = x^{3} + 3 x^{2} \cdot 5 + 3 x \cdot 5^{2} + 5^{3} = x^{3} + 15 x^{2} + 75 x + 125$

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Most popular questions from this chapter

In the following exercises, write with a rational exponent.

Part (a): $\sqrt[3]{25 a}$

Part (b): $\sqrt{3 b}$

Part (c): $\sqrt[8]{40 c}$

Factor completely: $27 y^{2} - 48$

In the following exercises, simplify each expression.

${(y^{4})}^{3} . {(y^{5})}^{2}$

Simplify::
(a) $36^{\frac{1}{2}}$

(b) $8^{\frac{1}{3}}$

(c) $16^{\frac{1}{4}}$

The number of hours it takes for ice to melt varies inversely with the air temperature. Suppose a block of ice melts in 2 hours when the temperature is 65 degrees Celsius.

Write the equation of variation.
How many hours would it take for the same block of ice to melt if the temperature was 78 degrees?

See all solutions

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