Factor completely. 20z^2-125 square

To factor the expression \(20z^2 - 125\) completely, we can follow these steps:<br /><br />1. **Identify the Greatest Common Factor (GCF):**<br /> The GCF of the terms \(20z^2\) and \(-125\) is 5.<br /><br />2. **Factor out the GCF:**<br /> \[<br /> 20z^2 - 125 = 5(4z^2 - 25)<br /> \]<br /><br />3. **Factor the remaining quadratic expression:**<br /> Notice that \(4z^2 - 25\) is a difference of squares. It can be factored as:<br /> \[<br /> 4z^2 - 25 = (2z)^2 - 5^2 = (2z - 5)(2z + 5)<br /> \]<br /><br />4. **Combine the factored terms:**<br /> \[<br /> 5(4z^2 - 25) = 5(2z - 5)(2z + 5)<br /> \]<br /><br />So, the completely factored form of \(20z^2 - 125\) is:<br />\[<br />\boxed{5(2z - 5)(2z + 5)}<br />\]