Question

Find each product. $$ -8 z\left(2 z+3 z^{2}+3 z^{3}\right) $$

   Find each product.
$$
-8 z\left(2 z+3 z^{2}+3 z^{3}\right)
$$

Beginning Algebra

Beginning Algebra

Margaret L. Lial,… 11th Edition

Chapter 5, Problem 19

Instant Answer

Solved by Expert Brandon Fox

06/22/2020

Step 1

This means we multiply $-8z$ by $2z$, $3z^{2}$, and $3z^{3}$ respectively. Show more…

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Find each product. $$ -8 z\left(2 z+3 z^{2}+3 z^{3}\right) $$

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Key Concepts

Distributive Property

The distributive property states that multiplying a sum by a single term is equivalent to multiplying each addend by that term and then summing the products. It is essential for expanding expressions and is used to multiply the -8z outside the parentheses by each term inside, ensuring no term is omitted.

Multiplication of Monomials

When multiplying monomials, you multiply the coefficients and then apply the laws of exponents to the variables. This concept is crucial as it allows us to combine the factors by adding the exponents of like bases during multiplication, which is a key step in simplifying polynomial expressions.

Polynomial Simplification

After the expansion of the product, polynomial simplification involves combining like terms and arranging the terms in a standard form, usually in order of decreasing degree. This process is necessary for obtaining a concise and easily understandable final result.

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