Simplify the Expression: 35m+9n-48m+52n Using Like Terms

To solve this problem, we'll follow these steps:

• Identify and group like terms within the expression.
• Combine the coefficients of these like terms.
• Simplify the expression by adding or subtracting coefficients.

Now, let's work through each step:

Step 1: Observe the given algebraic expression:
    $35m + 9n - 48m + 52n$.

Step 2: Group like terms, separating terms with $m$ from those with $n$:
    $(35m - 48m)$ and $(9n + 52n)$.

Step 3: Combine the terms with $m$:
    $35m - 48m = (35 - 48)m = -13m$.

Step 4: Combine the terms with $n$:
    $9n + 52n = (9 + 52)n = 61n$.

Therefore, the simplified form of the expression is:
    $61n - 13m$.

This leads to our final solution:

$61n - 13m$