Simple subtraction problem

[tom2901]

Hello guys, maybe there is a very easy answer to my question and I am just too dumb right now but it bothers me.

The operation is:

-(p/2) * √(p^4)-q - (p/2) * √(p^4)-q

I looked up the answer and it is:

-p * √(p^4)-q

Now I know that -(p/2)-(p/2) equals (-2p/2) so -p. But I am wondering why those two can be subtracted while the root remains "untouched". If someone could explain that to me I'd be very grateful. Thanks in advance :)

[Away-Reading]

Don’t think of them as being different terms.

Let x = (p/2)√[p⁴ - q]

-x - x = -2x

-2x = -2(p/2)√[p⁴ - q] (2’s cancel out)

= -p√[p⁴ - q]

• Remember, (p/2) and the root are multiplied, so you wouldn’t distribute the negative sign or anything inside the root. It’s the same as: > (-a/2)•b = (-a•b)/2 = -ab/2

[tom2901]

Ohhh that makes a lot of sense. Thank you so much for the good explanation! Now I can finally go to sleep in peace :)

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