How do you factor p^2+4p+4-q^2?

Jul 31, 2016

$\left(p + 2 + q\right) \left(p + 2 - q\right)$
${p}^{2} + 4 p + 4 - {q}^{2}$
$= {\left(p + 2\right)}^{2} - {q}^{2}$
Since ${a}^{2} - {b}^{2} - \left(a + b\right) \left(a - b\right)$
Similarly the above equation $= {\left(p + 2\right)}^{2} - {q}^{2}$ can be written as
$\left(p + 2 + q\right) \left(p + 2 - q\right)$