Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 5.4, Problem 15WE

To determine

To simplify the given expression.

Expert Solution & Answer

Answer to Problem 15WE

−1

Explanation of Solution

Given:

Expression: x2+2x−8(2−x)(4+x)

Concept used:

To simplify the given expression:

Take out common terms in the given expression.
Cancel out the terms that are in common in numerator and the denominator.
Find if any algebraic identities can simplify the given expression.

Calculation:

In the given expression find out the common term in the numerator and denominator.

⇒x2+2x−8(2−x)(4+x)

Consider the numerator and the denominator separately and factorize.

Consider the numerator and factorize.

⇒x2+2x−8⇒x2−2x+4x−8⇒(x2−2x)+(4x−8)⇒x(x−2)+4(x−2)⇒(x+4)(x−2)

Consider the denominator and factorize.

⇒(2−x)(4+x)

Substituting the factorized form of the numerator and the denominator in the given expression,

⇒(x+4)(x−2)(2−x)(4+x)⇒(x+4)(x−2)(2−x)(x+4)⇒(x+4)(x−2)(2−x)(x+4)⇒(x−2)(2−x)⇒(x−2)−(x−2)⇒(x−2)−(x−2)⇒−1

Conclusion:

Therefore, the simplified expression is −1.

Chapter 5.4, Problem 14WE

Chapter 5.4, Problem 16WE

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 5.1 - Prob. 1OE Ch. 5.1 - Prob. 2OE Ch. 5.1 - Prob. 3OE Ch. 5.1 - Prob. 4OE Ch. 5.1 - Prob. 5OE Ch. 5.1 - Prob. 6OE Ch. 5.1 - Prob. 7OE Ch. 5.1 - Prob. 8OE Ch. 5.1 - Prob. 9OE Ch. 5.1 - Prob. 10OE

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