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

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Answer 1 · 2018-03-05T00:12:03

The factored expression is #(x-2y)(x+2y)#.

You can write the expression as a difference of squares, then use a special factoring form:

#color(red)a^2-color(blue)b^2=(color(red)a-color(blue)b)(color(red)a+color(blue)b)#

Here's the actual problem:

#color(white)=x^2-4y^2#

#=x^2-2^2y^2#

#=(x)^2-(2y)^2#

#=(x-2y)(x+2y)#

That's as factored as it gets.