# How do you factor 16x^2-1?

Jun 1, 2016

$\left(4 x - 1\right) \left(4 x + 1\right)$

#### Explanation:

Both 16 and 1 are squares. This suggests using the formula for the difference of squares.

Jun 1, 2016

$16 {x}^{2} - 1 = \left(4 x + 1\right) \left(4 x - 1\right)$

#### Explanation:

$16 {x}^{2} - 1$ is of the form ${a}^{2} - {b}^{2}$ as $16 {x}^{2} = {\left(4 x\right)}^{2}$ and ${1}^{2} = 1$.

As such it can be factorized as $\left(a + b\right) \left(a - b\right)$ as such

$16 {x}^{2} - 1 = {\left(4 x\right)}^{2} - {1}^{2} = \left(4 x + 1\right) \left(4 x - 1\right)$

Jun 1, 2016

You factor it as a difference of two squares.

#### Explanation:

Every time you have a difference in the format of

${A}^{2} - {B}^{2}$ you can factor as $\left(A - B\right) \left(A + B\right)$.
Then you have to identify if your quantity is the difference of two squared quantities.
It is. In fact we can write it as:

$16 {x}^{2} - 1 = {\left(4 x\right)}^{2} - {1}^{2}$

Then we can apply our rule

${\left(4 x\right)}^{2} - {1}^{2} = \left(4 x - 1\right) \left(4 x + 1\right)$