Use this method when there are 4 terms and no common factor for all the terms:

\begin{align*} 3x + 2y + xy + 6 & = 3x + xy + 2y + 6 \qquad \quad [\text{Group terms}] \\ & = x(3 + y) + 2(y + 3) \\ & = x(y + 3) + 2(y + 3) \qquad [\text{Next, factorise } (y + 3) ]\\ & = (x + 2)(y + 3) \end{align*}

\begin{align*} 4x^2 - {1 \over 9}y^2 & = (2x)^2 - \left({1 \over 3}y\right)^2 \\ & = \left( 2x + {1 \over 3}y\right)\left(2x - {1 \over 3}y\right) \end{align*}

If you use the 'Solve quadratic equation' function in the calculator, ensure that $x^2$ is positive before using the calculator:

\begin{align*} -2x^2 + 3x + 9 & = -(2x^2 - 3x - 9) \qquad \phantom{.} \text{ [Enter } 2x^2 - 3x - 9 \text{ into calculator}] \\ & = - (x - 3)(2x + 3) \qquad \left[ x_1 = 3, x_2 = -{3 \over 2}\right] \end{align*}