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 expressions by eliminating the middle terms, resulting in a difference of squares. In the given expression, 4x and 7y are the two terms, allowing us to apply this rule directly.
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Difference of Squares
The difference of squares is a specific algebraic identity that states that the product of two conjugates results in the square of the first term minus the square of the second term. This concept is crucial for simplifying expressions like (4x + 7y)(4x - 7y), as it leads to a straightforward calculation of (4x)² - (7y)², which is 16x² - 49y².
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Algebraic Expressions
Algebraic expressions are combinations of numbers, variables, and operations. Understanding how to manipulate these expressions, including addition, subtraction, multiplication, and applying identities, is fundamental in algebra. In this case, recognizing the structure of the expression (4x + 7y)(4x - 7y) as a product of two binomials is essential for applying the appropriate multiplication rule.
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