Q. 12.69 Use the Binomial Theorem to expa... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 12.69 (page 1209)

Use the Binomial Theorem to expand ${(x + y)}^{5}$ .

Short Answer

Expert verified

The expanded form of the ${(x + y)}^{5}$ is $x^{5} + 5 x^{4} y + 10 x^{3} y^{2} + 10 x^{2} y^{3} + 5 x y^{4} + y^{5}$

Step by step solution

Step 1. Given information.

The given binomial is ${(x + y)}^{5}$ .

Step 2. Use the binomial theorem.

${(x + y)}^{5} = (\begin{matrix} 5 \\ 0 \end{matrix}) x^{5} + (\begin{matrix} 5 \\ 1 \end{matrix}) x^{4} y + (\begin{matrix} 5 \\ 2 \end{matrix}) x^{3} y^{2} + (\begin{matrix} 5 \\ 3 \end{matrix}) x^{2} y^{3} + (\begin{matrix} 5 \\ 4 \end{matrix}) x y^{4} + (\begin{matrix} 5 \\ 5 \end{matrix}) y^{5} w e k n o w, (\begin{matrix} n \\ 0 \end{matrix}) = (\begin{matrix} n \\ n \end{matrix}) = 1 a n d (\begin{matrix} n \\ 1 \end{matrix}) = n = x^{5} + 5 x^{4} y + \frac{5!}{2! (5 - 2)!} x^{3} y^{2} + \frac{5!}{3! (5 - 3)!} x^{2} y^{3} + \frac{5!}{4! (5 - 4)!} x y^{4} + y^{5} = x^{5} + 5 x^{4} y + \frac{5 脳 4 脳 3 脳 2 脳 1}{2 脳 1 脳 3 脳 2 脳 1} x^{3} y^{2} + \frac{5 脳 4 脳 3 脳 2 脳 1}{3 脳 2 脳 1 脳 2 脳 1} x^{2} y^{3} + \frac{5 脳 4 脳 3 脳 2 脳 1}{4 脳 3 脳 2 脳 1 脳 1} x y^{4} + y^{5} = x^{5} + 5 x^{4} y + 10 x^{3} y^{2} + 10 x^{2} y^{3} + 5 x y^{4} + y^{5}$

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91影视

Use the Binomial Theorem to expand ${(x + y)}^{5}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use the binomial theorem.

One App. One Place for Learning.

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91影视

Use the Binomial Theorem to expand x+y5.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use the binomial theorem.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Geometry

Study anywhere. Anytime. Across all devices.

Use the Binomial Theorem to expand ${(x + y)}^{5}$ .