How do I simplify this expression?

Question

Hey and thanks in advance,

I'm working on an optimization problem, and I've been studying for hours so my mind is slowly turning to mush. For whatever reason, I cannot figure out why this expression:

x² ((5-x²)/2x))

is simplified to this:

1/2(5x-x³)

I have a feeling I am missing something incredibly simple yet important, and I probably already know it but it's not registering and I am getting frustrated. Either way when I I attempt to simplify, the exponents do not add up and I need a simpler expression to be able to differentiate for the first and second derivative. GAAAAAHHHH

Rant over. But a million thanks to whoever helps me out!

JamesD · Accepted Answer

x² ((5-x²)/2x))
= [(x*x)/2x]*(5 - x²)
= (x/2)*(5 - x²)
= (1/2)*x*(5 - x²)
= (1/2)*(5x - x³)

Anonym · Answer

Can you show some examples of how you get to the wrong expression, so we can show you where you're going wrong?

How do I simplify this expression?

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