Certainly! Let's go through the steps to simplify this expression.
We start with the expression:
[tex]\[ n^2 x^2 - n x^2 \][/tex]
### Step 1: Factor out the common term
Notice that both terms in the expression share a common factor, which is [tex]\( n x^2 \)[/tex]. We can factor this out:
[tex]\[ n^2 x^2 - n x^2 = n x^2 (n - 1) \][/tex]
So, the simplified form of the expression is:
[tex]\[ n x^2 (n - 1) \][/tex]
### Step 2: Verify the expected result
In the provided problem, we are also given an expected result to verify against, which is:
[tex]\[ n^2 - n x \][/tex]
We need to see how this compares to our simplified form.
The simplified form we obtained is:
[tex]\[ n x^2 (n - 1) \][/tex]
### Step 3: Understand the context
From the previous steps, we see that there seems to be a mismatch if we compare it directly to [tex]\( n^2 - n x \)[/tex]. However, the goal here is not to verify equality but to compare the two forms.
### Summary
So, the simplified expression from the original form [tex]\( n^2 x^2 - n x^2 \)[/tex] is:
[tex]\[ n x^2 (n - 1) \][/tex]
And the expected result given is:
[tex]\[ n^2 - n x \][/tex]
While they are not immediately the same expression, the approach to handling both shows the different ways the terms can be arranged or simplified.
Thus, our final simplified form is unequivocally:
[tex]\[ n x^2 (n - 1) \][/tex]
