Question

factor $25y^2 - 15y$.

Explanation:

Step1: Find the GCF of coefficients and variables

The GCF of 25 and 15 is 5. For the variable part, the GCF of \(y^{2}\) and \(y\) is \(y\). So the GCF of \(25y^{2}\) and \(15y\) is \(5y\).

Step2: Divide each term by the GCF

Divide \(25y^{2}\) by \(5y\): \(\frac{25y^{2}}{5y}=5y\).
Divide \( - 15y\) by \(5y\): \(\frac{-15y}{5y}=-3\).

Step3: Write the factored form

Using the distributive property \(ab + ac=a(b + c)\), we get \(25y^{2}-15y = 5y(5y - 3)\).

Answer:

\(5y(5y - 3)\)