Find each product. (2z4-3y)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 50

1장, 문제 50

Find each product. (2z⁴-3y)²

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Recognize that the expression is a binomial squared: \((2z^4 - 3y)^2\). This means you will use the formula for the square of a binomial: \((a - b)^2 = a^2 - 2ab + b^2\).

Identify the terms: let \(a = 2z^4\) and \(b = 3y\).

Calculate the square of the first term: \(a^2 = (2z^4)^2 = 2^2 \cdot (z^4)^2 = 4z^{8}\).

Calculate twice the product of the two terms with a negative sign: \(-2ab = -2 \cdot (2z^4) \cdot (3y) = -12z^4 y\).

Calculate the square of the second term: \(b^2 = (3y)^2 = 9y^2\). Then, combine all parts to write the expanded expression: \(4z^{8} - 12z^4 y + 9y^2\).

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주요 개념

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

Polynomial Expressions

Polynomial expressions are algebraic expressions consisting of variables and coefficients combined using addition, subtraction, and multiplication, with non-negative integer exponents. Understanding the structure of polynomials helps in identifying terms and applying operations like expansion or factoring.

Binomial Squaring Formula

The binomial squaring formula states that (a - b)^2 = a^2 - 2ab + b^2. This formula is essential for expanding the square of a binomial expression, allowing you to rewrite it as a trinomial by squaring each term and doubling the product of the two terms.

Exponent Rules

Exponent rules govern how to handle powers of variables, such as multiplying powers by adding exponents and raising a power to another power by multiplying exponents. These rules are crucial when expanding expressions like (2z^4 - 3y)^2 to correctly simplify terms.