Explanation Procedure used: Factoring a expression Using the Greatest Common Factor: “Step 1: Identify the greatest common factor (GCF) of the terms of the polynomial. Step 2: Rewrite each term as the product of the GCF and the remaining factor. Step 3: Use the Distributive Property “in reverse” to factor out the GCF. Step 4: Check using the Distributive Property”. Calculation: Factor the given expression 2 a 2 − 2 b 2 + 4 c 2 − 6 d 2 as follows. Note that, the terms, 2 a 2 , 2 b 2 , 4 c 2 and 6 d 2 in the expression 2 a 2 − 2 b 2 + 4 c 2 − 6 d 2 has 4 p q as a common factor. That is, the GCF of the terms of the expression is 4 p q . Rewrite the terms 2 a 2 , 2 b 2 , 4 c 2 and 6 d 2 as the product of the GCF and the remaining factor then factor out the GCF as below. 2 a 2 − 2 b 2 + 4 c 2 − 6 d 2 = 2 ( a 2 ) + 2 ( − b 2 ) + 2 ( 2 c 2 ) 2 ( − 3 d 2 ) = 2 ( a 2 − b 2 + 2 c 2 − 3 d 2 ) [ Factor out the GCF ] That is, the expression 2 a 2 − 2 b 2 + 4 c 2 − 6 d 2 is factored into 2 ( a 2 − b 2 + 2 c 2 − 3 d 2 )

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 25E

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To factor: The given expression 2a2−2b2+4c2−6d2 completely.

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Chapter 6.1, Problem 24E

Chapter 6.1, Problem 26E

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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 2 a 2 − 2 b 2 + 4 c 2 − 6 d 2 completely.

Solution Summary: The author explains how to factor a given expression using the Greatest Common Factor.

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To factor: The given expression 2a2−2b2+4c2−6d2 completely.

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Chapter 6 Solutions