Textbook Question
Perform the indicated operation and write the answer in decimal notation.
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 36
Add or subtract terms whenever possible.
Verified step by step guidance1
Identify the like terms in the expression. Both terms have the radical \( \sqrt{13x} \), so they are like terms and can be combined.
Rewrite the expression to clearly show the coefficients and the radical: \( 4\sqrt{13x} - 6\sqrt{13x} \).
Combine the coefficients of the like terms by subtracting: \( 4 - 6 = -2 \).
Multiply the result by the common radical term: \( -2 \times \sqrt{13x} \).
Write the simplified expression as \( -2\sqrt{13x} \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Like Terms
Like terms are terms that have the same variable parts raised to the same powers. In this problem, terms involving √13x are like terms because they share the same radical expression. Only like terms can be added or subtracted by combining their coefficients.
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Simplifying Radicals
Simplifying radicals involves expressing the radical in its simplest form by factoring out perfect squares. Here, √13x is already simplified, so no further simplification is needed before combining terms. Recognizing simplified radicals helps in correctly identifying like terms.
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Combining Like Terms
Combining like terms means adding or subtracting their coefficients while keeping the variable or radical part unchanged. For example, 4√13x − 6√13x equals (4 − 6)√13x = −2√13x. This process simplifies expressions and is essential for solving algebraic problems efficiently.
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Related Practice
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