Q. 1.24 Expand (3x2聽+聽y)5.... [FREE SOLUTION]

91影视

A First Course in Probability

Sheldon M. Ross

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 432 pages

ISBN: 9780321794772

Chapter 1: Q. 1.24 (page 16)

Expand ${(3 x^{2} + y)}^{5}$ .

Short Answer

Expert verified

The value of ${(3 x^{2} + y)}^{5}$ is $y^{5} + 15 x^{2} y^{4} + 90 x^{4} y^{3} + 270 x^{6} y^{2} + 405 x^{8} y + 243 x^{10}$ .

Step by step solution

Step 1. Given information.

The given expression is ${(3 x^{2} + y)}^{5}$ .

Step 2. Expand the given expression.

Using the formula ${(a + b)}^{n} = {鈭�}_{x = 0}^{n} (\begin{matrix} n \\ x \end{matrix}) {(a)}^{n - x} {(b)}^{x}$

${(3 x^{2} + y)}^{5} = {鈭�}_{x = 0}^{5} (\begin{matrix} 5 \\ x \end{matrix}) {(3 x^{2})}^{5 - x} {(y)}^{x}$

$= (\begin{matrix} 5 \\ 0 \end{matrix}) {(3 x^{2})}^{5 - 0} {(y)}^{0} + (\begin{matrix} 5 \\ 1 \end{matrix}) {(3 x^{2})}^{5 - 1} {(y)}^{1} + (\begin{matrix} 5 \\ 2 \end{matrix}) {(3 x^{2})}^{5 - 2} {(y)}^{2} + (\begin{matrix} 5 \\ 3 \end{matrix}) {(3 x^{2})}^{5 - 3} {(y)}^{3} + (\begin{matrix} 5 \\ 4 \end{matrix}) {(3 x^{2})}^{5 - 4} {(y)}^{4} + (\begin{matrix} 5 \\ 5 \end{matrix}) {(3 x^{2})}^{5 - 5} {(y)}^{5} = 1 {(3 x^{2})}^{5} + 5 {(3 x^{2})}^{4} {(y)}^{1} + 10 {(3 x^{2})}^{3} {(y)}^{2} + 10 {(3 x^{2})}^{2} {(y)}^{3} + 5 {(3 x^{2})}^{1} {(y)}^{4} + 1 {(3 x^{2})}^{0} {(y)}^{5} = 243 x^{10} + 405 x^{8} y + 270 x^{6} y^{2} + 90 x^{4} y^{3} + 15 x^{2} y^{4} + y^{5}$

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91影视

Expand ${(3 x^{2} + y)}^{5}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Expand the given expression.

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91影视

Expand (3x2+y)5.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Expand the given expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Expand ${(3 x^{2} + y)}^{5}$ .