To factor the polynomial completely, first identify the greatest common factor (GCF) of all the terms. Then, factor out the GCF from the polynomial. Finally, check if the resulting expression can be factored further.
Step 1: Identify the Polynomial
We start with the polynomial:
50x4y−40x3y+8x2y
Step 2: Factor Out the Greatest Common Factor (GCF)
The GCF of the terms 50x4y, −40x3y, and 8x2y is 2x2y. We factor this out:
2x2y(2x2y50x4y−2x2y40x3y+2x2y8x2y)
This simplifies to:
2x2y(25x2−20x+4)
Step 3: Factor the Quadratic Expression
Next, we factor the quadratic expression 25x2−20x+4. This can be factored as:
(5x−2)2
Step 4: Combine the Factors
Combining the factors, we have:
2x2y(5x−2)2
Final Answer
Thus, the completely factored form of the polynomial is:
2x2y(5x−2)2