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}
$