What is the sum of like terms in the expression 5m - 2n + 3m + 4n?

• A. 8m + 2n
• B. 2m + 2n
• C. 8m + 6n
• D. 1m + 2n

Answer: (A)

To find the sum of like terms in the expression 5m - 2n + 3m + 4n, we first identify and group the like terms. Like terms are those that contain the same variable to the same degree.

In this expression, the terms containing the variable 'm' are 5m and 3m. To combine these, we add their coefficients:

5m + 3m = (5 + 3)m = 8m.

Next, we look at the terms containing the variable 'n', which are -2n and 4n. Similarly, we combine these by adding the coefficients:

-2n + 4n = (-2 + 4)n = 2n.

Now, we can write the combined expression by bringing together the results from the like terms:

8m + 2n.

This factorization effectively illustrates how to group and combine the coefficients of like terms, leading to the correct answer, which is the sum of both sets of like terms, resulting in 8m + 2n.