Why can 8(4x^2-y^2) be factored further but 8(4x^2+y^2) cannot be factored further

Question

precal · Answer

because the first case is a difference of squares and your second case is prime

sw050399 · Answer

Because the first function is a difference of squares; when you factor it out, and multiply it back together, the middle term cancels the other one out.

It doesn't work like that in the second function.

waheguru · Answer

Thanks

waheguru · Answer

CAn you explain what prime means

mertsj · Answer

Has no factors except for itself and 1

mertsj · Answer

We say that 7 is prime because its only factors are 7 x 1

waheguru · Answer

but cant the second one become 

8(4x^2+y^2)
8(2x+y)(2x+y) ????

waheguru · Answer

shouldn't that be the final factored form?

mertsj · Answer

Well why can't 7 become 3 x 5?

waheguru · Answer

One I said cannot be factoed any further because 8(2x+y)(2x+y) is not equavolent to 8(4x^2+y^2)
 I understand now

mertsj · Answer

Very good.  It has to multiply back.

waheguru · Answer

Thanks alot :)

precal · Answer

prime in this case, means it can not be factored