Question

Perform the operations. $$\left(-2 x^{2}\right)\left(3 x^{3}\right)$$

   Perform the operations.
$$\left(-2 x^{2}\right)\left(3 x^{3}\right)$$

Prealgebra

Alan S. Tussy, R.… 4th Edition

Chapter 10, Problem 41

Instant Answer

Solved by Expert Sherrie Fenner

07/21/2020

Step 1

The coefficient of $-2x^{2}$ is -2 and the coefficient of $3x^{3}$ is 3. So, $-2*3$ gives us -6. Show more…

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Perform the operations. $$\left(-2 x^{2}\right)\left(3 x^{3}\right)$$

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Key Concepts

Multiplication of Monomials

A monomial is an algebraic expression consisting of a single term. When multiplying monomials, both the coefficients and the variables (with exponents) are combined. This involves multiplying the coefficients and using the exponent rules to handle the variables, which is essential in simplifying polynomial expressions.

Multiplication of Coefficients

When multiplying two expressions, the numerical coefficients (the constant multipliers) are multiplied together separately. In algebra, this is done independently of the variable part, ensuring that the product of the coefficients is used in the combined expression.

Exponent Rules

When multiplying terms with the same base, the exponents are added. This rule states that for any base x and exponents m and n, x^m multiplied by x^n equals x^(m+n). It's a fundamental principle in simplifying algebraic expressions involving powers.

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