Textbook Question
Add or subtract terms whenever possible.
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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 42
Factor the difference of two squares.
Verified step by step guidance1
Recognize that the expression \(64x^2 - 81\) is a difference of two squares because it can be written as \((8x)^2 - 9^2\).
Recall the difference of squares formula: \(a^2 - b^2 = (a - b)(a + b)\).
Identify \(a = 8x\) and \(b = 9\) from the expression.
Apply the formula by substituting \(a\) and \(b\): \((8x - 9)(8x + 9)\).
Write the factored form of the expression as \((8x - 9)(8x + 9)\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Difference of Squares
The difference of squares is a specific algebraic expression of the form a² - b², which can be factored into (a - b)(a + b). Recognizing this pattern allows for straightforward factoring of expressions where two perfect squares are subtracted.
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Identifying Perfect Squares
To factor using the difference of squares, each term must be a perfect square. This means the terms can be expressed as the square of a number or variable, such as 64x² = (8x)² and 81 = 9², enabling the use of the difference of squares formula.
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Factoring Polynomials
Factoring polynomials involves rewriting an expression as a product of simpler expressions. Understanding how to factor special forms like the difference of squares is essential for simplifying expressions and solving equations in algebra.
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