In Exercises 15–58, find each product. (x−3)2

Ch. P - Fundamental Concepts of Algebra

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

문제 45

1장, 문제 45

In Exercises 15–58, find each product. (x−3)²

검증된 단계별 안내

Recognize that the expression \((x - 3)^2\) represents a binomial squared. This means you will expand it using the formula for the square of a binomial: \((a - b)^2 = a^2 - 2ab + b^2\).

Identify the terms in the binomial \((x - 3)\): here, \(a = x\) and \(b = 3\).

Apply the formula \((a - b)^2 = a^2 - 2ab + b^2\) to the given expression. Substitute \(a = x\) and \(b = 3\) into the formula.

Simplify each term: \(a^2 = x^2\), \(-2ab = -2(x)(3) = -6x\), and \(b^2 = 3^2 = 9\).

Combine the simplified terms to write the expanded form of the expression: \(x^2 - 6x + 9\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

Binomial Expansion

Binomial expansion refers to the process of expanding expressions that are raised to a power, particularly those in the form of (a + b)^n. In this case, (x - 3)^2 can be expanded using the formula (a - b)^2 = a^2 - 2ab + b^2, where a = x and b = 3. Understanding this concept is essential for correctly applying the expansion to find the product.

Square of a Binomial

The square of a binomial is a specific case of binomial expansion where a binomial expression is multiplied by itself. For (x - 3)^2, this means multiplying (x - 3) by (x - 3). The result will yield a quadratic expression, which is a polynomial of degree two. Recognizing this pattern helps in simplifying and solving similar algebraic expressions.

Quadratic Expressions

Quadratic expressions are polynomial expressions of the form ax^2 + bx + c, where a, b, and c are constants, and a is not zero. The result of expanding (x - 3)^2 will yield a quadratic expression. Understanding the structure of quadratic expressions is crucial for further analysis, such as factoring, graphing, or solving equations derived from them.