# How do you factor completely x^2 + 12xy + 35y^2?

${x}^{2} + 12 x y + 35 {y}^{2}$
$= {x}^{2} + 2. x .6 y + 35 {y}^{2}$
$= {x}^{2} + 2. x .6 y + {\left(6 y\right)}^{2} - {y}^{2}$
$= {\left(x + 6 y\right)}^{2} - {y}^{2}$
$= \left(x + 6 y + y\right) \cdot \left(x + 6 y - y\right)$
$= \left(x + 7 y\right) \left(x + 5 y\right)$