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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 199E (page 1213)

The expansion is $y^{5} + 10 y^{4} + 40 y^{3} + 80 y^{2} + 80 y + 32$

Short Answer

Expert verified

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

$(y + 2)^{5}$

Step by step solution

Given Information

Expand binomial using Pascal's Triangle.

$(y + 2)^{5}$

Solution

We have

Here the exponent is 5 hence we need to consider sixth row

The expansion is

$(y + 2)^{5} = 1 y^{5} + 5 y^{4} \cdot 2 + 10 y^{3} \cdot 2^{2} + 10 y^{2} \cdot 2^{3} + 5 y \cdot 2^{4} + 1 \cdot 2^{5} = y^{5} + 10 y^{4} + 40 y^{3} + 80 y^{2} + 80 y + 32$

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Most popular questions from this chapter

Find the sum of the first 50 terms of the arithmetic sequence whose general term is $a_{n} = 2 n - 5$ .

Determine if each sequence is arithmetic. If so, indicate the common difference.

$\begin{array}{l} (a) 9, 20, 31, 42, 53, 64, \dots \\ (b) 12, 6, 0, - 6, - 12, - 18, \dots \\ (c) 7, 1, 10, 4, 13, 7, \dots \end{array}$

In the following exercises, write the first five terms of each arithmetic sequence with the given first term and common difference.

$a_{1} = 8$ and $d = - 2$

In the following exercises, evaluate.

(a) $(\begin{array}{l} 3 \\ 1 \end{array})$ (b) $(\begin{array}{l} 9 \\ 9 \end{array})$ (c) $(\begin{array}{l} 7 \\ 0 \end{array})$ (d) $(\begin{array}{l} 5 \\ 3 \end{array})$

In the following exercises, write the first five terms of each arithmetic sequence with the given first term and common difference.

$a_{1} = 5$ and $d = 3$

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The expansion isy5+10y4+40y3+80y2+80y+32

Short Answer

Step by step solution

Given Information

Solution

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Most popular questions from this chapter

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The expansion is $y^{5} + 10 y^{4} + 40 y^{3} + 80 y^{2} + 80 y + 32$