How do you factor #4x^2-26#?

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Answer 1 · 2016-05-14T20:30:02

#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)#

The first term of our expression is a perfect square:

#4x^2 = (2x)^2#.

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

#26 = (sqrt(26))^2#

Hence we can factor:

#4x^2-26 = (2x)^2-(sqrt(26))^2 = (2x-sqrt(26))(2x+sqrt(26))#