How do you factor 4x^2-26?

May 14, 2016

$4 {x}^{2} - 26 = \left(2 x - \sqrt{26}\right) \left(2 x + \sqrt{26}\right)$

Explanation:

The difference of squares identity can be written:

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

The first term of our expression is a perfect square:

$4 {x}^{2} = {\left(2 x\right)}^{2}$.

The second term can be written as a square of its square root:

$26 = {\left(\sqrt{26}\right)}^{2}$

Hence we can factor:

$4 {x}^{2} - 26 = {\left(2 x\right)}^{2} - {\left(\sqrt{26}\right)}^{2} = \left(2 x - \sqrt{26}\right) \left(2 x + \sqrt{26}\right)$