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

Verified step by step guidance

1. Identify the expression to simplify: \(-2x^3(x^4 - 8)\).
2. Apply the distributive property, which means multiplying \(-2x^3\) by each term inside the parentheses separately.
3. Multiply \(-2x^3\) by \(x^4\): use the rule of exponents \(x^a \cdot x^b = x^{a+b}\) to combine the powers of \(x\).
4. Multiply \(-2x^3\) by \(-8\): multiply the coefficients and keep the variable part as is.
5. Write the simplified expression by combining the results from the two multiplications.

Key Concepts

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.