Find each product. [(3a+b)-1]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 55

1장, 문제 55

Find each product. [(3a+b)-1]²

검증된 단계별 안내

Recognize that the expression is a square of a binomial: \([(3a+b)-1]^2\). This can be rewritten as \((3a + b - 1)^2\).

Recall the formula for the square of a trinomial: \((x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2xz + 2yz\).

Identify the terms: \(x = 3a\), \(y = b\), and \(z = -1\).

Apply the formula by squaring each term and adding twice the product of each pair: \( (3a)^2 + b^2 + (-1)^2 + 2(3a)(b) + 2(3a)(-1) + 2(b)(-1) \).

Simplify each term and combine like terms to write the expanded form of the product.

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주요 개념

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

Exponent Rules

Exponent rules govern how to handle powers in algebraic expressions. For example, a negative exponent indicates the reciprocal of the base raised to the positive exponent, so (x)^-1 = 1/x. Understanding these rules is essential for simplifying expressions like [(3a + b)^-1]^2.

Binomial Expressions

A binomial is an algebraic expression with two terms, such as (3a + b). Recognizing binomials helps in applying operations like squaring or multiplying, which often involve using formulas like (x + y)^2 = x^2 + 2xy + y^2.

Power of a Power Property

The power of a power property states that (x^m)^n = x^(m*n). This means when raising a power to another power, you multiply the exponents. Applying this property simplifies expressions like [(3a + b)^-1]^2 to (3a + b)^-2.