To factor the expression xy³ x³y xyy xy x xyy xy x, we can first rewrite it as:
- xy³
- x³y
- xyy
- xy
- x
- xyy
- xy
- x
Now, let’s combine all the terms:
- xy³
- x³y = x² imes x imes y
- xyy = x imes y^2
- xy = x imes y
- x
- xyy = x imes y^2
- xy = x imes y
- x
Next, we can factor out common terms from the combined expression:
The least powers of each variable will help us factor:
- The least power of x present is x: and y is y.
- For y, the least power present is y² (taking two instances from y³, xy, and xyy).
So, the common term we can factor out is x²y²:
- xy³ can give us: y imes (y²)
- x³y can give us: x imes (x²y)
- xyy can give us: y imes (xy)
- xy can give us: (xy)
- x can remain as: (1)
Putting it all together, we can write the completely factored form as:
x²y²(xy² + x² + xy + x + 1)