Fuctorise \( 10 p^{3}+2 s^{2} y-8 r y^{2} \)

To factorize the expression \( 10 p^{3} + 2 s^{2} y - 8 r y^{2} \), follow these steps: 1. **Identify the Greatest Common Factor (GCF):** - Look for the highest common factor among the coefficients \(10\), \(2\), and \(-8\). - The GCF of \(10\), \(2\), and \(-8\) is \(2\). 2. **Factor Out the GCF:** \[ 10 p^{3} + 2 s^{2} y - 8 r y^{2} = 2 \left(5 p^{3} + s^{2} y - 4 r y^{2}\right) \] 3. **Check for Further Factorization:** - Examine the expression inside the parentheses: \(5 p^{3} + s^{2} y - 4 r y^{2}\). - There are no common factors among the terms \(5 p^{3}\), \(s^{2} y\), and \(-4 r y^{2}\). - Additionally, since the variables \(p\), \(s\), \(r\), and \(y\) are distinct, the expression does not factor further using standard factoring techniques. **Final Factorized Form:** \[ 2 \left(5 p^{3} + s^{2} y - 4 r y^{2}\right) \]