Textbook Question
Find each product : (4x+5)(4x-5)
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 77
State the name of the property illustrated. 6+(2+7)=(6+2)+7
Verified step by step guidance1
Identify the expression given: \(6 + (2 + 7) = (6 + 2) + 7\).
Notice that the numbers and the operation (addition) remain the same on both sides of the equation; only the grouping of the numbers changes.
Recall that the property which allows you to change the grouping of numbers in addition without changing the result is called the Associative Property of Addition.
The Associative Property of Addition states that for any numbers \(a\), \(b\), and \(c\), the equation \(a + (b + c) = (a + b) + c\) holds true.
Therefore, the given equation illustrates the Associative Property of Addition.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Associative Property of Addition
The associative property of addition states that when adding three or more numbers, the way in which the numbers are grouped does not affect the sum. For example, (a + b) + c = a + (b + c). This property allows us to change the grouping of addends without changing the result.
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Change of Base Property
Addition Operation
Addition is a fundamental arithmetic operation that combines two or more numbers to get their total or sum. Understanding how addition works is essential to grasp properties like associativity, as it involves manipulating sums without altering their values.
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Mathematical Properties in Algebra
Mathematical properties, such as associative, commutative, and distributive properties, describe consistent rules that apply to operations like addition and multiplication. Recognizing these properties helps simplify expressions and solve algebraic problems efficiently.
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Related Practice
Textbook Question
In Exercises 65–92, factor completely, or state that the polynomial is prime. 9x3−9x
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In Exercises 67–82, find each product. (x−y)(x2+xy+y2)
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Write each number in decimal notation without the use of exponents.
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In Exercises 69–82, simplify each complex rational expression. (3/(x−2) − 4/(x+2))/(7/x2−4)
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In Exercises 77–86, write each number in scientific notation. 64,000
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