Problem 42 Multiply out and simplify as com... [FREE SOLUTION]

91影视

Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 2: Problem 42

Multiply out and simplify as completely as possible. $$-4(m+r-v)$$

Short Answer

Expert verified

-4m - 4r + 4v

Step by step solution

- Distribute the -4

Multiply each term inside the parentheses by -4. This means you will perform the operation -4 * m, -4 * r, and -4 * (-v).

- Calculate the Products

Carry out the multiplication:-4 * m = -4m, -4 * r = -4r, and -4 * (-v) = 4v.

- Combine the Results

Combine all the terms from the products: -4m - 4r + 4v.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distribution in Algebra

Let's start by talking about distribution in algebra, which is a fundamental concept. When you see an expression like $-4(m + r - v)$, distribution means you'll multiply each term inside the parentheses by the number outside, in this case, -4.

Note how the number outside the parenthesis impacts every term inside.
This is essential since it keeps the expression equal to its original form.

For our exercise, you distribute -4 across $m + r - v$. This gives you three individual multiplication steps:
$-4 * m$, $-4 * r$, and $-4 * (-v)$.

Remember, the distribution process helps in breaking down complex expressions into simpler parts.

Multiplication of Terms

Next, let's dig into the multiplication of terms, another core concept relevant here. Whenever you multiply variables or numbers, you perform the operation directly:

Multiply the numbers while keeping track of the signs.
Negative multiplied by negative gives a positive.

In our problem, you need to multiply each term inside the parentheses individually by -4:

$ -4 * m = -4m $

$ -4 * r = -4r $

$ -4 * (-v) = 4v $.

Note how we've reversed the sign in $-4 * (-v) = 4v $ because multiplying two negatives results in a positive.

This is important as it ensures the final combined expression will be accurate.

Simplifying Expressions

Finally, once you have multiplied all terms, you need to simplify the expression. In algebra, simplifying means combining all your like terms to form the final, most straightforward expression.

Our example includes the terms \-4m\, \-4r\, and \4v\. Since there are no like terms to combine further, the simplified form of the expression is just:

$-4m - 4r + 4v $.

Simplifying expressions not only makes them easier to read but also helps in solving further algebraic problems. This step confirms you've correctly distributed and multiplied all terms previously.

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91影视

Multiply out and simplify as completely as possible. $$-4(m+r-v)$$

Short Answer

Step by step solution

- Distribute the -4

- Calculate the Products

- Combine the Results

Key Concepts

Distribution in Algebra

Multiplication of Terms

Simplifying Expressions

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