Problem 56 - Algebra 1

Question

Find the terms of the expression. $$ a+3 b-5 $$

Step-by-Step Solution

Answer

The terms of the expression \(a + 3b - 5\) are \(a\), \(3b\), and \(-5\).

Step 1: Identify terms separated by the addition operations

To get the terms of the given expression \(a + 3b - 5\), look for the parts separated by '+' or '-'. Here, each term is clearly separated by '+' and '-', irrespective of the sign before it. The first term in the expression is 'a'.

Step 2: Identify terms separated by the subtraction operations

The subtraction operation also separates terms. In this case, the second term is '3b', carrying the '+' sign from the previous '+' operation before it. Then, the last term will be '-5', taking into consideration the '-' sign before it.

Key Concepts

Terms of an Expression

In algebra, an expression is made up of several parts known as terms. Terms are essentially the building blocks of any algebraic expression. Each term can be a number, a variable, or the product of numbers and variables.
In the expression you are working with, terms are separated by addition or subtraction operators. For example, in the expression \(a + 3b - 5\), the terms are 'a', '3b', and '-5'.
Here are some ways to identify terms in an expression:

• Look for numbers or variables that stand alone.
• Recognize coefficients. In our example, the coefficient of 'b' in the term '3b' is 3.
• Be mindful of signs. The term '-5' includes the negative sign as part of the term.

Understanding terms helps you break down and simplify expressions effectively.

Addition of Terms

Adding terms is a fundamental operation in algebra. Not all terms are added straightforwardly; you must consider like terms when adding. Like terms are terms that contain the same variable raised to the same power. They can be combined by adding or subtracting their coefficients.
In our expression \(a + 3b - 5\), if you were to add another expression, like \(2a + 4b + 3\), you would only combine the like terms:

• Add the terms with 'a', which gives \(a + 2a = 3a\).
• Add the terms with 'b', resulting in \(3b + 4b = 7b\).
• Combine the constant terms \(-5 + 3 = -2\).

This leads to the new expression \(3a + 7b - 2\). Always check for like terms, as mixing different terms won't lead to simplification.

Subtraction of Terms

Subtracting terms works similarly to addition, but you must be cautious with the signs. Subtracting a positive term is like adding its negative counterpart, and vice versa.
Take the expression \(a + 3b - 5\) and subtract another expression, such as \(2a + 4b + 3\):

• Subtracting '2a' from 'a' gives you \(a - 2a = -a\).
• Subtracting '4b' from '3b' results in \(3b - 4b = -b\).
• Subtract the constant terms, \(-5 - 3 = -8\).

The resulting expression is \(-a - b - 8\). Always remember to apply the distributive property when necessary and be careful with negative signs to ensure accuracy.