Textbook Question
In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms.(2 − y⁵)(2 + y⁵)
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0. Review of Algebra
Polynomials Intro
1:35 minutesProblem 84
Textbook Question
Find each product. (x+7y)(3x-5y)
Verified step by step guidance1
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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Video duration:
1mKey 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 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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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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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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