# How do you factor the quadratic x^2-121?

Apr 30, 2018

${x}^{2} - 121 = \left(x + 11\right) \left(x - 11\right)$

#### Explanation:

As ${x}^{2}$ and $121 = {11}^{2}$ are both squares of $x$ and $11$ and there is minus sign between their squares,

we can use the identity ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

observe that factors of difference of squares ${a}^{2}$ and ${b}^{2}$ are sum of $a$ and $b$ and difference of $a$ and $b$

and then factors are sum of $x$ and $11$ and difference of $x$ and $11$

i.e. ${x}^{2} - 121 = \left(x + 11\right) \left(x - 11\right)$