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

Answer 1

Eli Assouline

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.

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Answer 2

Eli Assouline

(x^2 - 4y^2) can be factored using the difference of squares formula, which states that (a^2 - b^2 = (a + b)(a - b)). Applying this formula, we get ((x + 2y)(x - 2y)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.