Factoring with Two Variables

Property For a trinomial in the form $x^2 + bxy + cy^2$, find two terms that multiply to get $cy^2$ and add to get $bxy$. The factors will be in the form $(x + my)(x + ny)$. Explanation Seeing two variables might seem tricky, but it's just the same puzzle with a costume change! Ignore the $y$ for a moment and find two numbers that multiply to $c$ and add to $b$, just like always. Once you have your magic numbers, just attach a $y$ to each of them. Now they fit perfectly into the binomial factors. Easy peasy! Examples To factor $x^2 + 9xy + 14y^2$, find numbers that multiply to 14 and add to 9 (which are 2 and 7). The terms are $2y$ and $7y$, so the factors are $(x+2y)(x+7y)$. To factor $x^2 xy 20y^2$, find numbers that multiply to 20 and add to 1 (which are 5 and 4). The terms are $ 5y$ and $4y$, so the factors are $(x 5y)(x+4y)$.