Certainly! Let's simplify the expression step by step:
Given expression:
[tex]\[ x \cdot (-1) \cdot (-x) \cdot 1 \][/tex]
Step 1: Start by simplifying the factors that are constants:
[tex]\[ (-1) \cdot 1 = -1 \][/tex]
So, the expression becomes:
[tex]\[ x \cdot (-1) \cdot (-x) \cdot 1 = x \cdot (-1) \cdot (-x) = -x \cdot (-x) \][/tex]
Step 2: Now, look at the product of [tex]\(-x\)[/tex] and [tex]\(-x\)[/tex]:
[tex]\[ -x \cdot (-x) \][/tex]
When you multiply two negative numbers, the result is positive. Specifically, multiplying [tex]\(-x\)[/tex] by [tex]\(-x\)[/tex] gives:
[tex]\[ (-1) \cdot (-1) \cdot x \cdot x = 1 \cdot x^2 = x^2 \][/tex]
Therefore, the simplified expression is:
[tex]\[ x^2 \][/tex]
So, the simplified form of the given expression [tex]\( x \cdot(-1) \cdot(-x) \cdot(1) \)[/tex] is:
[tex]\[ \boxed{x^2} \][/tex]
