Subtract expression from another expression

1. Identify the expressions: The problem asks to subtract the expression $15mn - 22m + 2n$ from the expression $14mn - 12m + 7n$.
2. Set up the subtraction: To subtract one expression from another, we write the second expression minus the first expression. This is written as: $$(14mn - 12m + 7n) - (15mn - 22m + 2n)$$
3. Distribute the negative sign: When subtracting an expression, we distribute the negative sign to each term within the parentheses of the expression being subtracted. This changes the sign of each term.
$$14mn - 12m + 7n - 15mn + 22m - 2n$$
4. Group like terms: Now, we group the terms that have the same variables.
$$(14mn - 15mn) + (-12m + 22m) + (7n - 2n)$$
5. Combine like terms: Perform the addition or subtraction for each group of like terms.
For the $mn$ terms: $14mn - 15mn = -1mn = -mn$
For the $m$ terms: $-12m + 22m = 10m$
For the $n$ terms: $7n - 2n = 5n$
6. Write the final expression: Combine the results from step 5 to form the final simplified expression.
$$-mn + 10m + 5n$$