Q. 344 Expand the binomial using the Bi... [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. 344 (page 1222)

Expand the binomial using the Binomial Theorem.
${(4 x + 5 y)}^{3}$

Short Answer

Expert verified

On expanding the binomial, we get, ${(4 x + 5 y)}^{3} = 64 x^{3} + 240 x^{2} y + 300 x y^{2} + 125 y^{3}$ .

Step by step solution

Step 1. Given information.

Consider the given question,

${(4 x + 5 y)}^{3}$

Compare ${(a + b)}^{n}$ with the given expression,

$a = 4 x, b = 5 y, n = 3$

We use the Binomial Theorem,

localid="1645349379307" ${(a + b)}^{n} = (\begin{matrix} n \\ 0 \end{matrix}) a^{n} + (\begin{matrix} n \\ 1 \end{matrix}) a^{n - 1} 脳 b^{1} + (\begin{matrix} n \\ 2 \end{matrix}) a^{n - 2} 脳 b^{2} + . . . + (\begin{matrix} n \\ r \end{matrix}) a^{n - r} 脳 b^{r} + . . . + (\begin{matrix} n \\ n \end{matrix}) b^{n} . . . . . . 鈥� (i)$

Step 2. Substitute the values.

Substitute the values in equation (i),

${(4 x + 5 y)}^{3} = (\begin{matrix} 3 \\ 0 \end{matrix}) {(4 x)}^{3} + (\begin{matrix} 3 \\ 1 \end{matrix}) {(4 x)}^{3 - 1} 脳 {(5 y)}^{1} + (\begin{matrix} 3 \\ 2 \end{matrix}) {(4 x)}^{3 - 2} 脳 {(5 y)}^{2} + (\begin{matrix} 3 \\ 3 \end{matrix}) {(5 y)}^{3} {(4 x + 5 y)}^{3} = (1) {(4 x)}^{3} + (3) {(4 x)}^{2} (5 y) + \frac{3!}{2! (3 - 2)!} (4 x) {(5 y)}^{2} + (1) {(5 y)}^{3} {(4 x + 5 y)}^{3} = 64 x^{3} + 240 x^{2} y + 300 x y^{2} + 125 y^{3}$

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91影视

Expand the binomial using the Binomial Theorem.
${(4 x + 5 y)}^{3}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the values.

One App. One Place for Learning.

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91影视

Expand the binomial using the Binomial Theorem.4x+5y3

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the values.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Expand the binomial using the Binomial Theorem.
${(4 x + 5 y)}^{3}$