Problem 67 Multiply. $$ -3(2 x-y+z) $... [FREE SOLUTION]

Chapter 15: Problem 67

Multiply. $$ -3(2 x-y+z) $$

Short Answer

Expert verified

-6x + 3y - 3z

Step by step solution

- Distribute -3

Apply the distributive property of multiplication over addition and subtraction. Multiply -3 by each term inside the parentheses: \[ -3(2x) + -3(-y) + -3(z) \]

- Multiply Each Term

Now, perform the multiplication for each term: \[ -3 \times 2x = -6x \] \[ -3 \times -y = 3y \] \[ -3 \times z = -3z \]

- Combine the Results

Combine all the results from the multiplications: \[ -6x + 3y - 3z \]

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Key Concepts

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

Multiplication

In mathematics, multiplication is one of the basic operations of arithmetic. It involves combining numbers to get a product. In this exercise, we see multiplication applied through the distributive property.

Multiplication can be viewed as repeated addition. For example, multiplying 3 by 4 can be thought of as adding 3 four times: $3 + 3 + 3 + 3 = 12$.

When you multiply variables, you scale them. For instance, if you have $2x$ and multiply it by $-3$, it means you are scaling $2x$ by -3, which gives $-6x$. This concept is crucial in algebra to manipulate and solve equations.

Algebraic Expressions

Algebraic expressions are mathematical phrases that can contain numbers, variables, and operators (such as addition, subtraction, and multiplication). In our exercise, $2x - y + z$ is an algebraic expression.

An important skill in algebra is manipulating these expressions using properties like the distributive property.

The distributive property states that $a(b + c) = ab + ac$. It allows us to multiply each term inside the parenthesis by the factor outside. For the exercise, we use this property to distribute \-3\ into each term within the parenthesis:

$-3(2x)$ becomes $-6x$
$-3(-y)$ becomes $3y$
$-3(z)$ becomes $-3z$

Combining these, we get the final expression: $-6x + 3y - 3z$.

Negative Numbers

Negative numbers are numbers less than zero and are usually denoted with a minus sign (-). They represent a decrease or loss.

In our exercise, negative numbers play an essential role. Multiplying involves understanding the rules for negative numbers. Here are key points to remember:

Multiplying a positive number by a negative number results in a negative product. For example, $3 \times -2 = -6$.
Multiplying two negative numbers results in a positive product. For example, $-3 \times -2 = 6$.

For the given exercise, distributing \-3\ and multiplying by each term inside the parentheses gives us:

$-3 \times 2x = -6x$
$-3 \times -y = 3y$
$-3 \times z = -3z$

This understanding of negative numbers is crucial for performing algebraic operations accurately.

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91影视

Multiply. $$ -3(2 x-y+z) $$

Short Answer

Step by step solution

- Distribute -3

- Multiply Each Term

- Combine the Results

Key Concepts

Multiplication

Algebraic Expressions

Negative Numbers

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