Textbook Question
In Exercises 15–58, find each product. (7x3+5)(x2−2)
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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 32
Find each product. (x+5)(x−5)
Verified step by step guidance1
Recognize that the expression (x+5)(x-5) is a product of two binomials in the form of a difference of squares.
Recall the difference of squares formula: \(\\(a+b)(a-b) = a^2 - b^2\\)\).
Identify \(a = x\) and \(b = 5\) in the given expression.
Apply the formula by squaring each term: \(x^2\) and \$5^2$.
Write the product as \(x^2 - 25\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Binomial Expressions
A binomial is a polynomial with exactly two terms, such as (x + 5) or (x - 5). Understanding binomials is essential because the problem involves multiplying two binomials, which requires applying specific algebraic rules.
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Introduction to Algebraic Expressions
Product of Binomials
Multiplying two binomials involves using the distributive property (FOIL method) to multiply each term in the first binomial by each term in the second. This process expands the expression into a polynomial.
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03:41Special Products - Cube Formulas
Difference of Squares Formula
The expression (x + 5)(x - 5) is a classic example of the difference of squares, which states that (a + b)(a - b) = a² - b². Recognizing this pattern simplifies multiplication and helps quickly find the product.
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Related Practice
Textbook Question
In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. 9x2+5x−4
Textbook Question
Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √500x3/√10x-1
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Textbook Question
In Exercises 15–32, multiply or divide as indicated. (x3−25x)/4x2 ⋅ (2x2−2)/(x2−6x+5) ÷ (x2+5x)/(7x+7)
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Textbook Question
Simplify each exponential expression in Exercises 23–64.
Textbook Question
Find the union of the sets. {1,3,5,7}∪{2,4,6,8,10}
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