Explanation Factor the given expression x 4 − 16 as follows. Here, x 4 is the square of x 2 and 16 is the square of 4. The given binomial is difference of two squares Therefore, the expression can be written as ( x 2 ) 2 − ( 4 ) 2 . Factor the expression as follows. x 4 − 16 = ( x 2 ) 2 − ( 4 ) 2 = ( x 2 + 4 ) ( x 2 − 4 ) [ ∵ a 2 − b 2 = ( a + b ) ( a − b ) ] Thus, the expression x 4 − 16 is factored into ( x 2 + 4 ) ( x 2 − 4 ) . Consider the expression x 2 − 4 . The expression x 2 − 4 can be further factored as follows. Here, x 2 is the square of x and 4 is the square of 2. The binomial x 2 − 4 is the difference of two squares Therefore, the expression can be written as ( x ) 2 − ( 2 ) 2 . Factor the expression as follows

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 6.1, Problem 45E

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To factor: The given expression x4−16 completely.

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Chapter 6.1, Problem 44E

Chapter 6.1, Problem 46E

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Chapter 6 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 6.1 - Prob. 1PE Ch. 6.1 - Prob. 2PE Ch. 6.1 - Prob. 3PE Ch. 6.1 - Prob. 4PE Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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To factor: The given expression x 4 − 16 completely.

Solution Summary: The author explains how to factor the given expression x4-16 completely. The given binomial is the difference of two squares.

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To factor: The given expression x4−16 completely.

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Chapter 6 Solutions