Find each product. [(2m+7)-n]2

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 56

1장, 문제 56

Find each product. [(2m+7)-n]²

검증된 단계별 안내

Recognize that the expression \( [(2m+7) - n]^2 \) is a perfect square of a binomial, which can be expanded using the formula \( (a - b)^2 = a^2 - 2ab + b^2 \).

Identify \( a = (2m + 7) \) and \( b = n \) in the expression \( [(2m+7) - n]^2 \).

Apply the formula: \( [(2m+7) - n]^2 = (2m + 7)^2 - 2 \times (2m + 7) \times n + n^2 \).

Expand \( (2m + 7)^2 \) using the formula \( (x + y)^2 = x^2 + 2xy + y^2 \), where \( x = 2m \) and \( y = 7 \).

Write the full expanded expression by combining all terms: the square of \( 2m + 7 \), the product term \( -2(2m + 7)n \), and the square of \( n \).

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주요 개념

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

Binomial Expression

A binomial is an algebraic expression containing two terms connected by a plus or minus sign. In this problem, (2m + 7) - n is a binomial because it combines two terms, (2m + 7) and -n, which can be simplified or manipulated using algebraic rules.

Square of a Binomial

Squaring a binomial means multiplying the binomial by itself, such as (a - b)^2 = (a - b)(a - b). This expands to a^2 - 2ab + b^2, which is a key formula used to simplify expressions like [(2m + 7) - n]^2.

Distributive Property

The distributive property allows you to multiply each term inside a parenthesis by a term outside or in another parenthesis. It is essential for expanding products like (a - b)(a - b) by distributing each term properly to simplify the expression.