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Find the union of the sets. {e,m,p,t,y} ∪ ∅
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 1, Problema 35
Find each product. (5−7x)(5+7x)
Guida verificata passo dopo passo1
Recognize that the expression (5−7x)(5+7x) is a product of two binomials in the form (a−b)(a+b), which is a difference of squares pattern.
Recall the difference of squares formula: \(\\(a - b)(a + b) = a^2 - b^2\\)\).
Identify \(a = 5\) and \(b = 7x\) in the given expression.
Apply the formula by squaring each term: calculate \(a^2 = (5)^2\) and \(b^2 = (7x)^2\).
Write the product as \(5^2 - (7x)^2\), which simplifies to \(25 - 49x^2\).
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Binomial Multiplication
Binomial multiplication involves multiplying two expressions, each with two terms, such as (a + b)(c + d). The distributive property is used to multiply each term in the first binomial by each term in the second, combining like terms to simplify the result.
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Finding Zeros & Their Multiplicity
Difference of Squares
The difference of squares is a special product formula: (a - b)(a + b) = a² - b². It applies when multiplying conjugate binomials, resulting in the square of the first term minus the square of the second term, simplifying the multiplication process.
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06:24Solving Quadratic Equations by Completing the Square
Combining Like Terms
After multiplying binomials, terms with the same variable and exponent are combined to simplify the expression. This step ensures the final answer is in its simplest form, making it easier to interpret or use in further calculations.
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5:22Combinations
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