Textbook Question
Evaluate each exponential expression: 5-3• 5
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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 26
Find each product. (2x−5)(7x+2)
Verified step by step guidance1
Identify the two binomials to be multiplied: \((2x - 5)\) and \((7x + 2)\).
Apply the distributive property (also known as the FOIL method) to multiply each term in the first binomial by each term in the second binomial: First, Outer, Inner, Last.
Multiply the First terms: \(2x \times 7x = 14x^{2}\).
Multiply the Outer terms: \(2x \times 2 = 4x\) and the Inner terms: \(-5 \times 7x = -35x\).
Multiply the Last terms: \(-5 \times 2 = -10\), then combine like terms \$4x\( and \)-35x$ to simplify the expression.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Distributive Property
The distributive property allows you to multiply a single term by each term inside a parenthesis. For example, in (a + b)(c + d), you multiply each term in the first parenthesis by each term in the second. This property is essential for expanding products of binomials.
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Multiply Polynomials Using the Distributive Property
Multiplying Binomials
Multiplying binomials involves applying the distributive property twice or using the FOIL method (First, Outer, Inner, Last) to multiply each term in the first binomial by each term in the second. This process results in a polynomial expression.
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Combining Like Terms
After multiplying, you often get terms with the same variable and exponent. Combining like terms means adding or subtracting these terms to simplify the expression into its simplest polynomial form.
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Related Practice
Textbook Question
Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √48x3/√3x
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Textbook Question
In Exercises 15–32, multiply or divide as indicated. (x2−4)/(x−2) ÷ (x+2)/(4x−8)
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Textbook Question
Simplify each exponential expression in Exercises 23–64.
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Textbook Question
Evaluate each exponential expression: 2^(-4) + 4^(-1)
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Textbook Question
Find the intersection of the sets. {a,b,c,d}∩∅
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