Textbook Question
Simplify each exponential expression:
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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 28
In Exercises 15–58, find each product. (7x2−2)(3x2−5)
Verified step by step guidance1
Step 1: Recognize that the problem involves multiplying two binomials, (7x^2 - 2) and (3x^2 - 5). This can be solved using the distributive property, also known as the FOIL method (First, Outer, Inner, Last).
Step 2: Multiply the 'First' terms of each binomial: (7x^2) * (3x^2). This results in 21x^4.
Step 3: Multiply the 'Outer' terms of each binomial: (7x^2) * (-5). This results in -35x^2.
Step 4: Multiply the 'Inner' terms of each binomial: (-2) * (3x^2). This results in -6x^2.
Step 5: Multiply the 'Last' terms of each binomial: (-2) * (-5). This results in +10. Combine all these terms to form the expanded expression: 21x^4 - 35x^2 - 6x^2 + 10. Then simplify by combining like terms.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Multiplication
Polynomial multiplication involves distributing each term in the first polynomial to every term in the second polynomial. This process is often referred to as the FOIL method for binomials, but it generalizes to any polynomials. The goal is to combine like terms after distribution to simplify the expression.
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Distributive Property
The distributive property states that a(b + c) = ab + ac. This property is fundamental in algebra as it allows for the multiplication of a single term by a sum or difference. In the context of polynomials, it helps in expanding expressions by ensuring that each term is multiplied correctly.
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Combining Like Terms
Combining like terms is the process of simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. This step is crucial after multiplying polynomials, as it helps to reduce the expression to its simplest form, making it easier to interpret and work with.
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Related Practice
Textbook Question
In Exercises 15–32, multiply or divide as indicated. (x2+x)/(x2−4) ÷ (x2−1)/(x2+5x+6)
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Textbook Question
Simplify each exponential expression:
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Textbook Question
Evaluate each exponential expression: (33)/(36)
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Textbook Question
In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. 6x2−11x+4
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Textbook Question
Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0.
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