How do you factor $4 x^{2} - 26$ $4x^2-26$ ?

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Answer 1 · 2016-05-14T20:30:02

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

The difference of squares identity can be written:

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

The first term of our expression is a perfect square:

$4 x^{2} = {(2 x)}^{2}$ $4x^2 = (2x)^2$ .

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

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

Hence we can factor:

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

How do you factor 4x2−264x^2-26?