# How do you factor 9x^2+4y^2?

You can see $9 {x}^{2} + 4 {y}^{2}$as ${\left(3 x\right)}^{2} + {\left(2 y\right)}^{2}$.
Given the formula ${a}^{2} + {b}^{2} + 2 a b = {\left(a + b\right)}^{2}$ with $a = 3 x$ and $b = 2 y$ you have $2 a b = \left(2 \cdot 3 \cdot 2\right) x y = 12 x y$ so u can add and subtract it to have:
$= {\left(3 x\right)}^{2} + {\left(2 y\right)}^{2} + 12 x y - 12 x y = \left[{\left(3 x\right)}^{2} + {\left(2 y\right)}^{2} + 12 x y\right] - 12 x y = {\left(3 x + 2 y\right)}^{2} - 12 x y$