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In Exercises 83–90, perform the indicated operation or operations. (3x+4y)2−(3x−4y)2
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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 84
Find each product. (x+7y)(3x-5y)
Guida verificata passo dopo passo1
Identify the problem as the product of two binomials: \((x + 7y)(3x - 5y)\).
Apply the distributive property (also known as 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: \(x \times 3x = 3x^{2}\).
Multiply the Outer terms: \(x \times (-5y) = -5xy\).
Multiply the Inner terms: \(7y \times 3x = 21xy\), and multiply the Last terms: \(7y \times (-5y) = -35y^{2}\). Then combine like terms \(-5xy\) and \$21xy$.
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Distributive Property
The distributive property allows you to multiply each term inside one parenthesis by each term inside the other. It is essential for expanding expressions like (x + 7y)(3x - 5y) by distributing each term in the first binomial across the second.
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Multiply Polynomials Using the Distributive Property
Combining Like Terms
After expanding the product, you combine like terms, which are terms with the same variables raised to the same powers. This simplifies the expression into its simplest form, making it easier to interpret or use in further calculations.
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5:22Combinations
Multiplication of Variables and Coefficients
When multiplying terms like x and 3x or 7y and -5y, multiply the coefficients (numbers) and apply the laws of exponents to variables. For example, x * x = x², and coefficients multiply normally, which is crucial for correctly expanding the product.
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05:28Equations with Two Variables
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