Warning There is a checkbox at the bottom of the exam form that to be lost. Question 1 (Multiple Choice Worth 2 points) (Factoring Algebraic Expressions MC) Rewrite \( x^{4} y^{2}-3 x^{3} y^{3} \) using a common factor. \( 3 x y\left(x^{3} y-x^{2} y\right) \) \( 3 x y^{2}\left(x^{2}-x^{2} y\right) \) \( x^{2} y\left(x y-3 x y^{2}\right) \) \( x^{2} y^{2}\left(x^{2}-3 x y\right) \) Question 2(Multiple Choice Worth 2 points) (Factoring Algebraic Expressions LC) Previous Question

Let's factor the expression \( x^{4} y^{2} - 3 x^{3} y^{3} \) by identifying the greatest common factor (GCF) in each term. 1. **Identify the GCF:** - **For \(x\):** The smallest power of \(x\) in both terms is \(x^3\). - **For \(y\):** The smallest power of \(y\) in both terms is \(y^2\). So, the GCF is \(x^3 y^2\). 2. **Factor out the GCF:** \[ x^{4} y^{2} - 3 x^{3} y^{3} = x^{3} y^{2} (x - 3y) \] However, looking at the provided options, the closest matching factorization is: \[ x^{2} y^{2}\left(x^{2} - 3 x y\right) \] This can be verified by expanding: \[ x^{2} y^{2}\left(x^{2} - 3 x y\right) = x^4 y^2 - 3x^3 y^3 \] which matches the original expression. **Correct Answer:** \[ \boxed{ x^{2} y^{2}\left(x^{2}-3 x y\right) } \] This corresponds to the fourth option provided in the question.