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rjwjfw · Nov 11, 2013, 05:57 PM

I am trying to help my daughter with her Algebra homework but I forgot how to do this kind of problem: 8x squared - 50. She has to factor the problem completely.
I factored out a 2 which left me with 2(4x^2 - 25) but what next?

neodarwinian · Nov 11, 2013, 07:38 PM

That appears to be it.

There are no further common factors that I can see.

2(4X^2 - 25)
============This appears to be the fully factored expression. ( especially at the HS level )

ebaines · Nov 12, 2013, 09:13 AM

There is another step, recognizing that 4x^2-25 is the difference of two squares. Remember that:

$<br /> a^2 - b^2 = (a+b)(a-b)$

In this case setting a = 2x and b = 5 gives you:
$4x^2-25 = (2x)^2-5^2 = (2x+5)(2x-5)$

So the final answer is:

$<br /> 8x^2-50 = 2(2x-5)(2x+5)$