Perform the indicated operations. -2x3(x4-8)

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 8

1장, 문제 8

Perform the indicated operations. -2x³(x⁴-8)

검증된 단계별 안내

Identify the expression to simplify: \(-2x^3(x^4 - 8)\).

Apply the distributive property, which means multiplying \(-2x^3\) by each term inside the parentheses separately.

Multiply \(-2x^3\) by \(x^4\): use the rule of exponents \(x^a \cdot x^b = x^{a+b}\) to combine the powers of \(x\).

Multiply \(-2x^3\) by \(-8\): multiply the coefficients and keep the variable part as is.

Write the simplified expression by combining the results from the two multiplications.

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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 raised to whole-number exponents and coefficients. Understanding how to identify terms, coefficients, and exponents is essential for manipulating and simplifying polynomials.

Distributive Property

The distributive property states that multiplying a single term by a sum or difference inside parentheses involves multiplying the term by each addend separately. This property is key to expanding expressions like -2x^3(x^4 - 8).

Laws of Exponents

Laws of exponents govern how to multiply powers with the same base by adding their exponents. For example, when multiplying x^3 by x^4, the result is x^(3+4) = x^7. This rule is crucial for simplifying the product in the given expression.