# How do you factor 49x^2 - 121y^2?

May 4, 2015

$49 {x}^{2} - 121 {y}^{2}$ can be written as ${\left(7 x\right)}^{2} - {\left(11 y\right)}^{2}$

this is of the form:

${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

here: $a = 7 x$ and $b = 11 y$

so ,

${\left(7 x\right)}^{2} - {\left(11 y\right)}^{2} = \left(7 x + 11 y\right) \left(7 x - 11 y\right)$

the factorized form of $49 {x}^{2} - 121 {y}^{2}$ is:

$\left(7 x + 11 y\right) \left(7 x - 11 y\right)$