Let's work through the subtraction step by step.
We start with two expressions:
1. [tex]\( 14mn - 12m + 7n \)[/tex]
2. [tex]\( 15mn - 22m + 2n \)[/tex]
We need to subtract the second expression from the first one.
1. [tex]\( 14mn - 12m + 7n \)[/tex]
2. [tex]\(- (15mn - 22m + 2n) \)[/tex]
When we distribute the negative sign across the terms in the second expression, we get:
[tex]\[ - 15mn + 22m - 2n \][/tex]
Now, we can rewrite the subtraction as an addition of the negated second expression to the first expression:
[tex]\[ (14mn - 12m + 7n) + (- 15mn + 22m - 2n) \][/tex]
Next, combine like terms:
1. Combine the [tex]\( mn \)[/tex] terms:
[tex]\[ 14mn - 15mn = -mn \][/tex]
2. Combine the [tex]\( m \)[/tex] terms:
[tex]\[ -12m + 22m = 10m \][/tex]
3. Combine the [tex]\( n \)[/tex] terms:
[tex]\[ 7n - 2n = 5n \][/tex]
Thus, when we combine all these results, we get:
[tex]\[ -mn + 10m + 5n \][/tex]
Therefore, the final simplified result of subtracting [tex]\( 15mn - 22m + 2n \)[/tex] from [tex]\( 14mn - 12m + 7n \)[/tex] is:
[tex]\[ -mn + 10m + 5n \][/tex]
