Simplify the expression 4m+5+2m-1
The Correct Answer and Explanation is:
To simplify the expression 4m+5+2m−14m + 5 + 2m – 14m+5+2m−1, we need to combine like terms.
Step 1: Identify like terms
- The terms involving the variable mmm are 4m4m4m and 2m2m2m.
- The constant terms are 555 and −1-1−1.
Step 2: Combine like terms
- Combine the mmm-terms: 4m+2m=6m4m + 2m = 6m4m+2m=6m.
- Combine the constants: 5−1=45 – 1 = 45−1=4.
Step 3: Write the simplified expression
After combining like terms, we have: 6m+46m + 46m+4
This is the simplified form of the original expression 4m+5+2m−14m + 5 + 2m – 14m+5+2m−1.
Explanation
In algebra, simplifying expressions is about making them as concise as possible by combining like terms. Like terms are terms that have the same variable raised to the same power (e.g., 4m4m4m and 2m2m2m are like terms because they both contain the variable mmm raised to the first power). Constants (numbers without variables) are also like terms and can be combined.
To combine terms, we simply add or subtract the coefficients (the numerical factors in front of the variables) for the like terms. For instance:
- In 4m+2m4m + 2m4m+2m, we add the coefficients (4 and 2) to get 6, resulting in 6m6m6m.
- In 5−15 – 15−1, we subtract the constants to get 4.
So, 4m+5+2m−14m + 5 + 2m – 14m+5+2m−1 simplifies to 6m+46m + 46m+4.
The simplified expression is now easier to work with and is considered the most efficient representation of the original expression.
