Sure, let's work through the problem step-by-step to find the difference of the polynomials:
Given polynomials:
[tex]\[
(10m - 6) - (7m - 4)
\][/tex]
First, distribute the negative sign through the second polynomial:
[tex]\[
10m - 6 - (7m - 4) = 10m - 6 - 7m + 4
\][/tex]
Rearrange the terms to group the like terms together:
[tex]\[
(10m - 7m) + (-6 + 4)
\][/tex]
Now, let's simplify each group:
[tex]\[
10m - 7m = 3m
\][/tex]
[tex]\[
-6 + 4 = -2
\][/tex]
So, the simplified expression is:
[tex]\[
3m - 2
\][/tex]
Next, we need to identify the correct expression from the provided options that represents this simplified form.
Examining the options:
- [tex]\((10m + (-7m)) + [(-6) + 4] \)[/tex]
- [tex]\((10m + 7m) + [(-6) + (-4)] \)[/tex]
- [tex]\([(-10m) + (-7m)] + (6 + 4) \)[/tex]
- [tex]\((10m + (-7m)) + [6 + (-4)] \)[/tex]
Comparing our simplified form [tex]\(3m - 2\)[/tex] to break it down:
[tex]\[
10m - 7m = 3m
\][/tex]
[tex]\[
-6 + 4 = -2
\][/tex]
The correct option that represents this form is:
[tex]\[
[10 m + (-7 m)] + [(-6) + 4]
\][/tex]
Thus, the expression that can be used to find the difference of the given polynomials is:
[tex]\[
[10 m + (-7 m)] + [(-6) + 4]
\][/tex]
