Perform the indicated operations. -2x^3(x^4-8)

Key Concepts

Polynomial Operations

Polynomial operations involve performing arithmetic operations such as addition, subtraction, multiplication, and division on polynomial expressions. In this case, we are focusing on multiplication, where each term in one polynomial is multiplied by each term in another polynomial, following the distributive property.

Distributive Property

The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by each term within a parenthesis. This property is essential for simplifying expressions, as it helps in expanding polynomials by distributing the term outside the parentheses across all terms inside.

Exponent Rules

Exponent rules govern how to handle powers of variables during multiplication and division. For instance, when multiplying like bases, you add the exponents (a^m * a^n = a^(m+n)). Understanding these rules is crucial for simplifying expressions involving variables raised to powers, especially when dealing with polynomials.