Problem 25 - Prealgebra

Question

Simplify expression. \(4+2 m+m\)

Step-by-Step Solution

Answer

The simplified expression is \(3m + 4\).

Step 1: Identify Like Terms

In the expression given, take a look at the terms and identify those that are like terms. In this case, both terms containing the variable 'm', namely '2m' and 'm', are like terms. The constant term '4' is a standalone term.

Step 2: Combine Like Terms

Combine these identified like terms by adding their coefficients. The coefficients for the like terms '2m' and 'm' are 2 and 1, respectively. Thus, the sum is: \(2m + m = 3m\).

Step 3: Write the Simplified Expression

Once the like terms are combined, rewrite the expression by placing the resultant term next to any constant terms. Thus, the simplified expression is \(3m + 4\).

Key Concepts

Understanding Like Terms

In the world of algebra, like terms are terms that contain the same variable raised to the same power. Understanding like terms is crucial when simplifying expressions. For example, in the expression \(4 + 2m + m\), both \(2m\) and \(m\) contain the variable 'm' and are therefore like terms. The term \(4\), however, does not have any variables attached, making it a constant term and not similar to the others. Identifying like terms is the first step in simplifying expressions because they are the terms that we can directly combine through addition or subtraction.

To quickly spot like terms, look for terms that:

• Have the same variable(s).
• Have the same exponent(s) on these variables.

The Art of Combining Like Terms

Once you've identified like terms in an expression, the next task is to combine them. This is a straightforward process that involves adding or subtracting the coefficients, which are the numerical parts of the terms. The variable part of the terms does not change. Consider the coefficients of \(2m\) and \(m\), which are 2 and 1 respectively.

By adding these coefficients together, \(2 + 1\), we end up with \(3m\). Essentially, combining like terms helps condense an expression, making it more manageable and easier to work with.

Remember:

• Combine terms with the same variable by adding or subtracting their coefficients.
• Keep the variable part unchanged.

Mastering Mathematical Expressions

Mathematical expressions are combinations of numbers, variables, and operation symbols. Simplifying these expressions by combining like terms is an essential skill in algebra that helps you solve equations and perform calculations more efficiently. For our example, \(4 + 2m + m\), we have:

• The term '4', which is a constant.
• Like terms '2m' and 'm'.

The final step in simplifying is to rewrite the expression as \(3m + 4\), where the like terms have been combined and the constant is added for completeness.

As you become more adept at spotting and combining like terms, working with algebraic expressions will become second nature. Always:

• Start by identifying like terms within the expression.
• Combine them to simplify the expression.
• Rewrite the expression to clearly display the simplified form.