DaddyKadyn
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Which expression can be used to find the difference of the polynomials?

(10m - 6) - (7m - 4)

A. [tex]\[(10m + (-7m)) + (-6 + 4)\][/tex]
B. [tex]\[(10m + 7m) + (-6 + (-4))\][/tex]
C. [tex]\[(-10m + (-7m)) + (6 + 4)\][/tex]
D. [tex]\[(10m + (-7m)) + (6 + (-4))\][/tex]

Sagot :

GinnyAnswer
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]
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