Questions: Complete the factoring of the polynomial. 25 x^2 y^3 + 20 x^2 y^2 = 5 x^2 y^2

Solution Steps

To factor the given polynomial, we need to find the greatest common factor (GCF) of the terms and factor it out. The GCF of \(25 x^{2} y^{3}\) and \(20 x^{2} y^{2}\) is \(5 x^{2} y^{2}\). We then divide each term by the GCF and write the polynomial as a product of the GCF and the resulting polynomial.

We start with the polynomial given by \[ 25 x^{2} y^{3} + 20 x^{2} y^{2}. \]

The GCF of the terms \(25 x^{2} y^{3}\) and \(20 x^{2} y^{2}\) is \[ 5 x^{2} y^{2}. \]

We factor out the GCF from the polynomial: \[ 25 x^{2} y^{3} + 20 x^{2} y^{2} = 5 x^{2} y^{2} \left(5y + 4\right). \]

Final Answer