Step by step explanation plz (shouldn't be complicated)

manniman

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Hello, I'm currently doing some calculus but my algebra is horrible. Anyway, I'm looking at the solution manual in one of the problems and I don't understand how this expression in one step --> 1 + (0.5x^4 - 0.5x^-4)^2 turns into this expression in the next step --> (0.5x^4 + 0.5x^.4)^2.

Basically what's in the parenthesis goes from a subtraction to a sum (which is what I need for the particular problem, I just don't know why or the steps to get there algebraically step by step). It probably has something to do with the 1 but I don't know how to get rid of the 1.

Thank you so much. Remember, I suck at algebra so step by step explanation would be appreciated.
 
Hello, I'm currently doing some calculus but my algebra is horrible. Anyway, I'm looking at the solution manual in one of the problems and I don't understand how this expression in one step --> 1 + (0.5x^4 - 0.5x^-4)^2 turns into this expression in the next step --> (0.5x^4 + 0.5x^.4)^2.

Basically what's in the parenthesis goes from a subtraction to a sum (which is what I need for the particular problem, I just don't know why or the steps to get there algebraically step by step). It probably has something to do with the 1 but I don't know how to get rid of the 1.

Thank you so much. Remember, I suck at algebra so step by step explanation would be appreciated.
LOOK HERE
 
I know there are other forms and I have looked at other sites that give the same answer as the one you linked but that is not the form that I'm looking for. I need to know the algebraic manipulation that the book did to get from this 1 + (0.5x^4 - 0.5x^-4)^2 to this specific form (0.5x^4 + 0.5x^4)^2 .
 
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Hello, I'm currently doing some calculus but my algebra is horrible. Anyway, I'm looking at the solution manual in one of the problems and I don't understand how this expression in one step --> 1 + (0.5x^4 - 0.5x^-4)^2 turns into this expression in the next step --> (0.5x^4 + 0.5x^.4)^2.

Basically what's in the parenthesis goes from a subtraction to a sum (which is what I need for the particular problem, I just don't know why or the steps to get there algebraically step by step). It probably has something to do with the 1 but I don't know how to get rid of the 1.

Thank you so much. Remember, I suck at algebra so step by step explanation would be appreciated.
First expand (0.5x^4 - 0.5x^-4)^2, either using the fact that (a+b)^2 = a^2 + 2ab + b^2, or using "FOIL" on (0.5x^4 - 0.5x^-4)(0.5x^4 - 0.5x^-4).

Then add 1 to what you get.

Then expand (0.5x^4 + 0.5x^.4)^2 similarly and compare.

Those are the steps. You get to do them, in order to learn. But it isn't all about getting rid of the 1; that sort of gets absorbed along the way by accident.
 
First expand (0.5x^4 - 0.5x^-4)^2, either using the fact that (a+b)^2 = a^2 + 2ab + b^2, or using "FOIL" on (0.5x^4 - 0.5x^-4)(0.5x^4 - 0.5x^-4).

Then add 1 to what you get.

Then expand (0.5x^4 + 0.5x^.4)^2 similarly and compare.

Those are the steps. You get to do them, in order to learn. But it isn't all about getting rid of the 1; that sort of gets absorbed along the way by accident.
Thank you. Yes, I had to foil it to get (0.25x^8 - 1/2 + 0.25x^-8), then ADD the ONE to get (0.25x^8 + 1/2 + 0.25x^-8)...

From there I had to realize that the difference of the original terms, squared, became a sum of of those same terms, squared, when I add the 1. I think that's only possible because the coefficients of the terms in the original subtraction is 1/2 (0.5)
 
Did you try to square the terms on each side and then collect like terms? Most students can NOT look at what you posted and say oh yeah they are obviously equal. You need to investigate a bit.
 
Thank you. Yes, I had to foil it to get (0.25x^8 - 1/2 + 0.25x^-8), then ADD the ONE to get (0.25x^8 + 1/2 + 0.25x^-8)...

From there I had to realize that the difference of the original terms, squared, became a sum of of those same terms, squared, when I add the 1. I think that's only possible because the coefficients of the terms in the original subtraction is 1/2 (0.5)
You've got it exactly.
 
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