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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. 238 (page 1214)

In your own words, explain the difference between ${(a + b)}^{n}$ and ${(a - b)}^{n}$ .

Short Answer

Expert verified

The expression ${(a + b)}^{n}$ represents the $n th$ power of the sum of two numbers. The expression ${(a - b)}^{n}$ represents the $n th$ power of the difference between two numbers.

Step by step solution

01

Step 1. Given information.

We have:

${(a + b)}^{n} {(a - b)}^{n}$

02

Step 2. Find the difference between given epressions.

The binomial expansion formula is given by:

${(x + y)}^{n} = {}^{n}C_{0} x^{n} y^{0} + {}^{n}C_{1} x^{n - 1} y^{1} + {}^{n}C_{2} x^{n - 2} y^{2} + . . . + {}^{n}C_{n} x^{0} y^{1}$

Suppose $a$ and $b$ are two numbers. The difference between these numbers is given by:

$a - b$

Multiply the difference $(a - b), n$ times with itself gives:

${(a - b)}^{n}$

Therefore, ${(a - b)}^{n}$ represents the nth power of the difference between two numbers.

Similarly, the sum of $a$ and $b$ is given by:

$(a + b)$

Multiplying the sum $(a + b), n$ times with itself gives:

${(a + b)}^{n}$

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