To find the difference of the given polynomials, we start with the expression:
[tex]\[
(10m - 6) - (7m - 4)
\][/tex]
The first step in subtracting these polynomials is to distribute the negative sign across the second polynomial:
[tex]\[
(10m - 6) - 7m + 4
\][/tex]
Next, we combine the like terms. This involves subtracting \(7m\) from \(10m\) to combine the \(m\) terms, and adding \(-6\) and \(4\) to combine the constant terms:
1. For the \(m\) terms:
[tex]\[
10m - 7m = 3m
\][/tex]
2. For the constant terms:
[tex]\[
-6 + 4 = -2
\][/tex]
So, the simplified polynomial after performing the subtraction is:
[tex]\[
3m - 2
\][/tex]
Next, we want to determine which provided expression represents this simplification process:
- \([10m + (-7m)] + [(-6) + 4]\)
- \((10m + 7m) + [(-6) + (-4)]\)
- \([(-10m) + (-7m)] + (6 + 4)\)
- \([10m + (-7m)] + [6 + (-4)]\)
Let's analyze each option to see which matches our steps.
1. \([10m + (-7m)] + [(-6) + 4]\)
- This correctly corresponds to \((10m - 7m)\) for the \(m\) terms and \((-6) + 4\) for the constants.
- Result: \(3m - 2\).
2. \((10m + 7m) + [(-6) + (-4)]\)
- This suggests combining \(10m + 7m\) and \((-6) + (-4)\), which does not match our subtraction process.
3. \([(-10m) + (-7m)] + (6 + 4)\)
- This suggests a negative conditional, which doesn't align with our initial polynomials.
4. \([10m + (-7m)] + [6 + (-4)]\)
- For the \(m\) terms \((10m + (-7m) = 3m\)), this is correct, but the constants \((6 + (-4))\) don't match our constants \( (-6 + 4)\).
Thus, the expression that correctly simplifies the given polynomial is:
[tex]\[
\boxed{[10m + (-7m)] + [(-6) + 4]}
\][/tex]
