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In Exercises 83–90, perform the indicated operation or operations. (3x+4y)2−(3x−4y)2
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 1, Problema 85
In Exercises 83–90, perform the indicated operations. Simplify the result, if possible. (2−6/(x+1))(1 + 3/(x−2))
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Distribute the terms in the expression (2 - 6/(x+1))(1 + 3/(x-2)) using the distributive property: multiply each term in the first parenthesis by each term in the second parenthesis.
The first multiplication is 2 * 1, which simplifies to 2.
The second multiplication is 2 * (3/(x-2)), which simplifies to 6/(x-2).
The third multiplication is (-6/(x+1)) * 1, which simplifies to -6/(x+1).
The fourth multiplication is (-6/(x+1)) * (3/(x-2)), which simplifies to -18/((x+1)(x-2)). Combine all these terms into a single expression and simplify further if possible.
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Algebraic Expressions
Algebraic expressions are mathematical phrases that can include numbers, variables, and operators. Understanding how to manipulate these expressions is crucial for performing operations such as addition, subtraction, multiplication, and division. In the given question, the expressions involve fractions and require simplification, which is a common task in algebra.
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Introduction to Algebraic Expressions
Multiplication of Fractions
Multiplying fractions involves multiplying the numerators together and the denominators together. This concept is essential for simplifying expressions that contain fractions, as seen in the problem. Recognizing how to handle fractions correctly ensures accurate results when performing operations on algebraic expressions.
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05:45Radical Expressions with Fractions
Simplification of Expressions
Simplification is the process of reducing an expression to its simplest form. This involves combining like terms, reducing fractions, and eliminating unnecessary parentheses. In the context of the question, simplifying the result after performing the indicated operations is key to presenting a clear and concise answer.
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05:09Introduction to Algebraic Expressions
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