Textbook Question
In Exercises 55–68, multiply using one of the rules for the square of a binomial.(5x − 3y)²
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0. Review of Algebra
Polynomials Intro
2:07 minutesProblem 70
Textbook Question
In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms.(x + 5)(x − 5)
Verified step by step guidance1
Identify the expression as a product of the sum and difference of two terms: \((x + 5)(x - 5)\).
Recall the formula for the product of the sum and difference of two terms: \((a + b)(a - b) = a^2 - b^2\).
In this expression, identify \(a = x\) and \(b = 5\).
Apply the formula: substitute \(a\) and \(b\) into \(a^2 - b^2\) to get \(x^2 - 5^2\).
Simplify the expression by calculating \(5^2\) to complete the expression \(x^2 - 25\).
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2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Product of Sum and Difference
The product of the sum and difference of two terms follows the formula (a + b)(a - b) = a² - b². This identity simplifies the multiplication of binomials by eliminating the middle terms, resulting in a difference of squares. Understanding this concept allows for quicker calculations and a clearer grasp of polynomial identities.
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Binomial Multiplication
Binomial multiplication involves multiplying two binomials, which are algebraic expressions containing two terms. The process can be executed using the distributive property or special product formulas, such as the one for the product of the sum and difference. Mastery of this concept is essential for simplifying expressions and solving equations in algebra.
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Difference of Squares
The difference of squares is a specific algebraic identity that states a² - b² can be factored into (a + b)(a - b). This concept is crucial in algebra as it provides a method for factoring quadratic expressions and solving equations. Recognizing this pattern helps in simplifying complex expressions and understanding polynomial behavior.
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