Questions: Factor the polynomial completely. 50 x^4 y-40 x^3 y+8 x^2 y=

Solution Steps

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.

We start with the polynomial: \[ 50 x^{4} y - 40 x^{3} y + 8 x^{2} y \]

The GCF of the terms \(50 x^{4} y\), \(-40 x^{3} y\), and \(8 x^{2} y\) is \(2 x^{2} y\). We factor this out: \[ 2 x^{2} y \left( \frac{50 x^{4} y}{2 x^{2} y} - \frac{40 x^{3} y}{2 x^{2} y} + \frac{8 x^{2} y}{2 x^{2} y} \right) \] This simplifies to: \[ 2 x^{2} y (25 x^{2} - 20 x + 4) \]

Next, we factor the quadratic expression \(25 x^{2} - 20 x + 4\). This can be factored as: \[ (5 x - 2)^{2} \]

Combining the factors, we have: \[ 2 x^{2} y (5 x - 2)^{2} \]

Final Answer