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Chapter 11: Problem 2

For problems 1 and 2 specify each term. $$ 8 m-2 n-4 $$

Short Answer

Expert verified
The terms are \(8m\), \(-2n\), and \(-4\).

Step by step solution

01

Identify Each Term

To solve the expression \(8m - 2n - 4\), we should first identify each term in the expression. Each term is separated by a plus or minus sign. Here, the terms are: \(8m\), \(-2n\), and \(-4\).
02

Classify Each Term

Next, classify each term according to its components. - **\(8m\)** is a linear term involving the variable \(m\) with a coefficient of 8. - **\(-2n\)** is another linear term involving the variable \(n\) with a coefficient of -2. - **\(-4\)** is a constant term, meaning it does not involve any variables.

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Key Concepts

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

Terms in Algebra
In algebra, expressions are composed of individual parts known as terms. A term can be a single number, a variable, or numbers and variables multiplied together.
For example, let's consider the expression given:
  • It contains three main terms: \(8m\), \(-2n\), and \(-4\).
  • Each term is distinct, separated by a plus or minus sign.
Terms form the building blocks of algebraic expressions, allowing us to perform operations and simplify expressions.
Coefficients
The coefficient in a term is the numerical factor multiplied by the variable within that term. Think of it as the number that "sits in front" of the variable.
  • In the term \(8m\), the coefficient is \(8\). This means that \(m\) has been multiplied by \(8\).
  • Similarly, in the term \(-2n\), the coefficient is \(-2\), indicating that \(n\) is multiplied by \(-2\).
  • It's essential to note the sign in front of the coefficient, as it impacts the algebraic operation being performed.
Coefficients are crucial in determining the magnitude and direction (positive or negative) of a term in relation to other terms.
Constant Term
A constant term is unique because it does not involve any variable; it's just a number. In algebraic expressions, this term represents a fixed value.
In the given expression:
  • The term \(-4\) is the constant term.
  • This means it stands alone without any variable attached.
Constant terms can significantly affect the overall value of an expression and are unaffected by changes in variable values. Understanding constant terms helps in evaluating algebraic expressions.
Linear Terms
Linear terms are those that involve variables raised to the power of one. Such terms indicate a linear relationship between variables.
In our expression:
  • \(8m\) is a linear term because the variable \(m\) is raised to the first power.
  • Similarly, \(-2n\) is another linear term as the variable \(n\) is also raised to the first power.
  • Linear terms are simple yet foundational in algebra, paving the way for understanding linear equations and functions.
Recognizing linear terms allows students to better grasp algebraic expressions and solve equations effectively.

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Most popular questions from this chapter

For problems \(57-140\), solve each equation. $$ \frac{3 y}{2}-4=6 $$

For problems \(57-140\), solve each equation. $$ 4 x=24 $$

Translate each phrase or sentence to a mathematical expression or equation. A number is subtracted from nine. This result is then increased by one. The result is eight more than three times the number.

Translate each phrase or sentence to a mathematical expression or equation. Three less than some number is equal to twice the number minus six.

For problems \(57-140\), solve each equation. $$ \frac{-3 m}{2}+1=5 m $$
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