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Chapter 1: Problem 33

Simplify each algebraic expression by combining similar terms. $$4 m+m-8 m$$

Short Answer

Expert verified
-3m

Step by step solution

01

Identifying Similar Terms

In this expression, we have the terms \(4m\), \(m\), and \(-8m\). These are similar terms because they have the same variable, \(m\). Thus, we can combine them.
02

Combining Coefficients

Combine the coefficients of the similar terms. The coefficients are 4, 1, and -8. Therefore, we have: \(4 + 1 - 8\).
03

Calculating the Result

Calculate \(4 + 1 - 8\), which simplifies to \(-3\).
04

Writing the Simplified Expression

Since the coefficients sum to \(-3\), the simplified expression is \(-3m\).

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Key Concepts

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

Combining Like Terms
When simplifying algebraic expressions, one of the key steps is to combine like terms. Like terms are terms that have the exact same variables raised to the same power. In the given expression, the terms are \(4m\), \(m\), and \(-8m\). They are all like terms because they only contain the variable \(m\).

Combining like terms involves adding or subtracting their coefficients. Think of it as gathering apples. If you have 4 apples, 1 more apple, and then you lose 8 apples, you're left with a deficit of apples. In the same way, we combine \(4m\), \(m\), and \(-8m\) by adding their coefficients together: \(4+1-8\). This step drastically simplifies your expression.
Coefficients
In algebra, coefficients are the numerical part of the terms. They are the numbers that are multiplied by the variables in each term. In our example with the expression \(4m + m - 8m\), the coefficients are 4, 1, and -8.

Knowing how to manipulate coefficients is crucial for simplifying expressions. Here鈥檚 how you handle them:
  • Addition: When combining, simply add the coefficients of like terms.
  • Subtraction: If there鈥檚 a minus sign, subtract the coefficients.
So, for this exercise, you do \(4 + 1 - 8\). Coefficients bring life to your variables, turning abstract expressions into concrete numbers to calculate.
Algebra Basics
Understanding the basics of algebra is essential for tackling any mathematical problem. Algebra often involves variables鈥攕ymbols like \(m\) used in place of numbers鈥攃ombined with constants or coefficients.

Simplifying algebraic expressions by combining like terms is fundamental in algebra. This is because it consolidates the terms to make calculations easier and expressions simpler.

Key points include:
  • Identifying Terms: Pinpoint the parts of your expression.
  • Determining Like Terms: Look for terms with identical variables and powers.
  • Using Arithmetic: Apply basic addition and subtraction to combine coefficients.
Practicing these basics will help you become comfortable with more complex algebraic concepts eventually.

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Most popular questions from this chapter

Simplify each algebraic expression by combining similar terms. $$-9 y+5 y-7 y$$

State the property that justifies each statement. For example, \(3+(-4)=(-4)+3\) because of the commutative property for addition. $$-119+119=0$$

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$(4)(-16)(-9)(-25)$$

Simplify each algebraic expression by combining similar terms. $$-2(m+3)-3(m-1)+8(m+4)$$

Find the value of \(\frac{h\left(b_{1}+b_{2}\right)}{2}\) for each set of values for the variables \(h, b_{1}\), and \(b_{2}\). (Subscripts are used to indicate that \(b_{1}\) and \(b_{2}\) are different variables.) \(h=14, b_{1}=9\), and \(b_{2}=7\)
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