step 1 In this problem, we're being asked to multiply the monomial 4W squared by the trinomial 3W to th

Question

$$ 4 w^{2}\left(3 w^{3}-2 w^{2}-w\right) $$

Name: Problem 25, Chapter 10: Algebra 1: Concepts and Skills
Uploaded: 2020-04-17T01:32:40-08:00
Duration: 41 s
Channel: Julie Silva
Description: 4 w^2(3 w^3-2 w^2-w)

   $$
4 w^{2}\left(3 w^{3}-2 w^{2}-w\right)
$$

Algebra 1: Concepts and Skills

Ron Larson, Laurie… 1st Edition

Chapter 10, Problem 25

Instant Answer

Solved by Expert Julie Silva

04/17/2020

Step 1

This is done by multiplying the coefficients (4 and 3) and adding the exponents of w (2 and 3). This gives us $12w^{5}$. Show more…

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$$ 4 w^{2}\left(3 w^{3}-2 w^{2}-w\right) $$

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Key Concepts

Distributive Property

This property allows you to multiply a single term by each term inside a grouping symbol, such as parentheses. It is essential in expanding expressions like a(b + c + d), which results in ab + ac + ad.

Laws of Exponents

The laws of exponents govern how to handle terms with the same base when multiplying. Specifically, when multiplying like bases, you add their exponents, as seen when multiplying w^m * w^n to get w^(m+n).

Polynomial Multiplication

This process involves multiplying terms of polynomials together using methods such as distribution and exponent rules. It is a fundamental concept in algebra for simplifying and expanding polynomial expressions.

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