Find each product. (4m+2n)2

Ch. R - Review of Basic Concepts

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

모든 교과서

Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 47

1장, 문제 47

Find each product. (4m+2n)²

검증된 단계별 안내

Recognize that the expression \( (4m + 2n)^2 \) is a binomial squared, which can be expanded using the formula for the square of a sum: \( (a + b)^2 = a^2 + 2ab + b^2 \).

Identify \( a = 4m \) and \( b = 2n \) in the expression \( (4m + 2n)^2 \).

Calculate \( a^2 \) by squaring \( 4m \), which means squaring both the coefficient and the variable: \( (4m)^2 = 4^2 \times m^2 \).

Calculate \( 2ab \) by multiplying 2, \( a = 4m \), and \( b = 2n \): \( 2 \times 4m \times 2n \).

Calculate \( b^2 \) by squaring \( 2n \): \( (2n)^2 = 2^2 \times n^2 \), then combine all parts to write the expanded form: \( a^2 + 2ab + b^2 \).

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.

Binomial Square Formula

The binomial square formula states that (a + b)^2 = a^2 + 2ab + b^2. It is used to expand the square of a sum of two terms by squaring each term and adding twice their product.

Distributive Property

The distributive property allows multiplication over addition, meaning a(b + c) = ab + ac. This property is essential when expanding expressions like (4m + 2n)^2 by distributing each term properly.

Combining Like Terms

After expanding an expression, like terms (terms with the same variable and exponent) must be combined to simplify the result. This step ensures the final expression is in its simplest form.