Find each product. (2m+3)(2m-3)

검증된 단계별 안내

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 $4m^2 - 9$.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

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.

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.

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.