Textbook Question
In Exercises 35–54, use the FOIL method to multiply the binomials.(3y−4)(2y−1)
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0. Review of Algebra
Polynomials Intro
2:11 minutesProblem 43
Textbook Question
Find each product. (2m+3)(2m-3)
Verified step by step guidance1
Recognize that the expression (2m+3)(2m-3) 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 \(a = 2m\) and \(b = 3\) from the given binomials.
Apply the formula by squaring each term: calculate \(\\left(2m\\right)^2\) and \$3^2$ separately.
Write the product as \(\\left(2m\\right)^2 - 3^2\), which simplifies to \$4m^2 - 9$.
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Video duration:
2mKey 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 (2m + 3)(2m - 3) by multiplying 2m by both terms in the second parenthesis and then 3 by both terms.
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Difference of Squares
The expression (a + b)(a - b) is a special product called the difference of squares, which simplifies to a² - b². Recognizing this pattern helps quickly find the product without full expansion, such as (2m + 3)(2m - 3) = (2m)² - 3².
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Combining Like Terms
After expanding an expression, combining like terms means adding or subtracting terms with the same variable and exponent. This step simplifies the expression to its simplest form, making it easier to interpret or use in further calculations.
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