I have no idea how to solve this. Can someone please help me for a medal? :) (posting below)

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I have no idea how to solve this. Can someone please help me for a medal? :) (posting below)

Mathematics
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\[\frac{ f(x+Δx)−f(x) }{ Δx }\] if f(x) = x^2
compute as \(\huge \frac{(x + \Delta x)^2 - x^2}{\Delta x}\)
so expand out the \(\large (x + \Delta x)^2\) in the numerator :p

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I know how to get to the expanding part, but I am not sure how to expand the numerator. Could you show me how?
Would it end up looking like this... \[\frac{ x^{2} + Δx^{2}-x^{2} }{ Δx } \]
first expand out \( (x+Δx)^2\) on its own that's \( (x+Δx) \times (x+Δx)\)
|dw:1440705634106:dw|
That makes sense, but how do you multiple an "Δx" by an "x"
\(x \times \Delta x = x \ \Delta x\)
So the numerator would end up being... \[\frac{ x^{2}+2xΔx+Δx^{2}-x^{2} }{ Δx }\] which would simplify to... \[\frac{ 2xΔx+Δx^{2} }{ Δx }\] is that correct?
\[\checkmark\]
now finish it!
\[\frac{ Δx(2x+Δx) }{ Δx }\] And the final answer would be... 2x+Δx ?
yay! well done learning calculus? happy days!
Thank you so much. :)
any time! thank you.

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