Find each product. [(9r-s)+2][(9r-s)-2]

검증된 단계별 안내

Recognize that the expression is in the form of a product of two binomials: \([(9r - s) + 2][(9r - s) - 2]\). This matches the pattern of a difference of squares: \((a + b)(a - b) = a^2 - b^2\).

Identify \(a\) and \(b\) in the expression: here, \(a = (9r - s)\) and \(b = 2\).

Apply the difference of squares formula: \((9r - s)^2 - 2^2\).

Expand the square of the binomial \((9r - s)^2\) using the formula \((x - y)^2 = x^2 - 2xy + y^2\), where \(x = 9r\) and \(y = s\).

Write the final expression as \(81r^2 - 18rs + s^2 - 4\), combining all parts without simplifying further.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Difference of Squares

The difference of squares is a special product formula expressed as (a + b)(a - b) = a² - b². It allows quick multiplication of two binomials that are conjugates, simplifying the expression by subtracting the square of the second term from the square of the first.

Binomial Expressions

A binomial is an algebraic expression containing two terms connected by addition or subtraction. Understanding how to manipulate binomials, including addition, subtraction, and multiplication, is essential for simplifying expressions and solving equations.

Exponentiation of Algebraic Terms

Exponentiation involves raising variables or expressions to a power, such as squaring a binomial term. Knowing how to correctly apply exponents to variables and constants is crucial for expanding and simplifying algebraic expressions.