Beginning Algebra With Applications, Chapter 8, 8.1, Section 8.1, Problem 124

Factor by grouping

a. $3x^2 + 3xy - xy - y^2$


$\begin{equation} \begin{aligned} 3x^2 + 3xy - xy - y^2 =& (3x^2 + 3xy) - (xy + y^2) && \text{Group the first two terms and the last two terms} \\ =& 3x(x+y) - y(x+y) && \text{Factor out the GCF from each group} \\ =& (3x-y)(x+y) && \text{Write the expression as a product of factors} \end{aligned} \end{equation}$


b. $3x^2 - xy + 3xy - y^2$


$\begin{equation} \begin{aligned} 3x^2 - xy + 3xy - y^2 =& (3x^2 - xy) + (3xy - y^2) && \text{Group the first two terms and the last two terms} \\ =& x(3x-y) + y(3x-y) && \text{Factor out the GCF from each group} \\ =& (x+y)(3x-y) && \text{Write the expression as a product of factors} \end{aligned} \end{equation}$