Find each product. (x+5)(x−5)

검증된 단계별 안내

Recognize that the expression (x+5)(x-5) is a product of two binomials in the form of a difference of squares.

Recall the difference of squares formula: $\\(a+b)(a-b) = a^2 - b^2\$\).

Identify $a = x$ and $b = 5$ in the given expression.

Apply the formula by squaring each term: $x^2$ and \$5^2$.

Write the product as $x^2 - 25$.

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주요 개념

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

Binomial Expressions

A binomial is a polynomial with exactly two terms, such as (x + 5) or (x - 5). Understanding binomials is essential because the problem involves multiplying two binomials, which requires applying specific algebraic rules.

Product of Binomials

Multiplying two binomials involves using the distributive property (FOIL method) to multiply each term in the first binomial by each term in the second. This process expands the expression into a polynomial.

Difference of Squares Formula

The expression (x + 5)(x - 5) is a classic example of the difference of squares, which states that (a + b)(a - b) = a² - b². Recognizing this pattern simplifies multiplication and helps quickly find the product.