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Chapter 0: Problem 19

Simplify each expression. $$ -8 z+4 w $$

Short Answer

Expert verified
-8z + 4w

Step by step solution

01

- Identify Like Terms

Recognize and separate the terms in the expression. Here, -8z and 4w are the terms. Note that they are not like terms since they have different variables.
02

- Check for Combinability

Determine if the terms can be combined. Since -8z and 4w have different variables, they cannot be combined.
03

- Present the Simplified Form

Since the terms cannot be combined, the simplified form of the expression is -8z + 4w.

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Key Concepts

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

Like Terms
In algebra, it is crucial to understand the concept of like terms.
Like terms have exactly the same variables raised to the same power.
For example, consider the terms 1. 3x and 5x (both have the variable 'x')
2. -2y and y (both have the variable 'y')
Like terms can be combined by adding or subtracting their coefficients.
On the other hand, terms like 4w and 7z are unlike terms because they have different variables ('w' and 'z').
When simplifying expressions, always look for like terms and combine them.
Variables
Variables are symbols used to represent numbers.
Common variables include letters like x, y, and z.
A variable can stand for any value within a given set.
In the expression -8z + 4w, 'z' and 'w' are variables.
Variables are often accompanied by coefficients (numbers in front of them).
The variable itself can be any number, but the expression is simplified by combining like terms, not by solving for the variable's value.
Combining Terms
Combining terms refers to the process of adding or subtracting like terms in an algebraic expression.
Follow these steps to combine terms: 1. Identify the terms in the expression.
2. Separate and group like terms together.
3. Add or subtract the coefficients of like terms.
For instance, in the expression -8z + 4w, 1. The terms are -8z and 4w.
2. Since they have different variables ('z' and 'w'), they cannot be combined.
When there are no like terms to combine, the expression must be left in its original form.
Practice identifying and combining like terms to ease simplifying complex expressions!

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