Textbook Question
In Exercises 39–48, factor the difference of two squares. 16x4−81
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 47
Add or subtract terms whenever possible. 7√5 + 13√5
Verified step by step guidance1
Identify the like terms in the expression. Here, both terms have the radical \( \sqrt{5} \), so they are like terms.
Rewrite the expression by factoring out the common radical \( \sqrt{5} \): \( 7\sqrt{5} + 13\sqrt{5} = (7 + 13)\sqrt{5} \).
Add the coefficients of the like terms inside the parentheses: \( 7 + 13 \).
Express the simplified form as the product of the sum of coefficients and the common radical: \( (7 + 13)\sqrt{5} \).
Leave the expression in this simplified form without calculating the final numeric value.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Like Terms in Algebra
Like terms are terms that have the same variable parts raised to the same powers. In the context of radicals, terms with the same radicand (number under the root) are considered like terms and can be combined by adding or subtracting their coefficients.
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Simplifying Algebraic Expressions
Simplifying Radicals
Simplifying radicals involves expressing the root in its simplest form by factoring out perfect squares or cubes. This process helps identify like terms and makes it easier to combine them when adding or subtracting.
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5:48Adding & Subtracting Unlike Radicals by Simplifying
Addition and Subtraction of Radical Expressions
When adding or subtracting radical expressions, only like radicals (same radicand and root) can be combined by adding or subtracting their coefficients. For example, 7√5 + 13√5 equals (7 + 13)√5 = 20√5.
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Related Practice
Textbook Question
Evaluate each expression or indicate that the root is not a real number.
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Determine whether each statement is true or false. -π ≥ - π
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Rationalize the denominator.
Textbook Question
In Exercises 15–58, find each product. (4x2−1)2
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Textbook Question
Add or subtract as indicated. 2/5x − (x+1)/4x
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