To find the completely factored form of the expression xy³ + x³y + xyy + xy + x + xyy + xy + x, we first need to reorganize the terms for clarity. Let’s rewrite the expression:
- xy³
- x³y
- xyy
- xy
- x
- xyy (again)
- xy (again)
- x (again)
Now, combining like terms, we have:
- xy³
- 2 * xyy
- 2 * xy
- 2 * x
- x³y
Next, let’s factor out the common factors from each term. Notice that x is a common factor:
Factoring out x gives us:
- x(yyx + xy² + 2yy + 2y + x²y)
Now, we need to make sure to simplify the expression inside the parentheses:
The expression becomes:
- x(yyx + xy² + 2yy + 2y + x²y)
At this stage, factoring further may not simplify the expression easily without a specific numeric or additional context about desired factors. Therefore, the completely factored form of the original expression is:
x(yyx + xy² + 2yy + 2y + x²y)
This gives us insight into the structure of the original polynomial, demonstrating common factors and helping in further calculations or evaluations. Remember to check if it can be simplified further based on particular values of variables involved.