Q 23. Expand x2+y25聽using Binomial Th... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q 23. (page 836)

Expand ${(x^{2} + y^{2})}^{5}$ using Binomial Theorem

Short Answer

Expert verified

The value of ${(x^{2} + y^{2})}^{5} = x^{10} + 5 x^{8} y^{2} + 10 x^{2} y^{4} + 10 x^{4} y^{6} + 5 x^{2} y^{8} + y^{10}$

Step by step solution

Step 1. Defination

Let $x$ and $a$ be realnumber forany positive integer $n$ , we have ${(x + a)}^{n} = (\begin{matrix} n \\ 0 \end{matrix}) x^{n} + (\begin{matrix} n \\ 1 \end{matrix}) a x^{n - 1} + 鈰� 鈰� + (\begin{matrix} n \\ j \end{matrix}) a^{j} x^{n - j} + 鈰� 鈰� + (\begin{matrix} n \\ n \end{matrix}) a^{n} = {鈭�}_{j = 0}^{n} (\begin{matrix} n \\ j \end{matrix}) x^{n - j} a^{j}$

Step 2. Explanation

$鈬� {(x^{2} + y^{2})}^{5} = (\begin{matrix} 5 \\ 0 \end{matrix}) {(y^{2})}^{0} {(x^{2})}^{5} + (\begin{matrix} 5 \\ 1 \end{matrix}) {(y^{2})}^{1} {(x^{2})}^{4} + (\begin{matrix} 5 \\ 2 \end{matrix}) {(y^{2})}^{2} {(x^{2})}^{3} + (\begin{matrix} 5 \\ 3 \end{matrix}) {(y^{2})}^{3} {(x^{2})}^{2} + (\begin{matrix} 5 \\ 4 \end{matrix}) {(y^{2})}^{4} {(x^{2})}^{1} + (\begin{matrix} 5 \\ 5 \end{matrix}) {(y^{2})}^{5} {(x^{2})}^{0}$

$鈬� {(x^{2} + y^{2})}^{5} = x^{10} + 5 x^{8} y^{2} + 10 x^{2} y^{4} + 10 x^{4} y^{6} + 5 x^{2} y^{8} + y^{10}$

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91影视

Expand ${(x^{2} + y^{2})}^{5}$ using Binomial Theorem

Short Answer

Step by step solution

Step 1. Defination

Step 2. Explanation

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91影视

Expand x2+y25using Binomial Theorem

Short Answer

Step by step solution

Step 1. Defination

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Decision Maths

Mechanics Maths

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

Expand ${(x^{2} + y^{2})}^{5}$ using Binomial Theorem