Help expanding (x+Δx)²

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vissuumm

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Hi, I'm just starting out learning this type of maths and I am confused about this answer:
(x+Δx) * (x+Δx)
= x² + 2x Δx + (Δx)²

I don't understand why it isn't:
x² + Δx² + Δx² + (Δx)²

Where does the 2x come from? Isn't x * Δx = Δx² ?

Really appreciate any help, thanks!
 
Why didn't you ask the question from the beginning? Wouldn't your conclusion also mean x+Δx = x(1+Δ)? That may be a useful notation, but you should find it confusing at this moment.

Generally, though Δx indicates a process and not a multiplication.

How would you expand (x+log(x))(x+log(x))?

Alternatively, Δx means a differential. It is not meaningful if you separate the two characters.
 
vissuumm said:
Hi, I'm just starting out learning this type of maths and I am confused about this answer:
(x+Δx) * (x+Δx)
= x² + 2x Δx + (Δx)²
Click to expand...
To do pre-calculus or calculus one needs a good foundation in basic algebra.
\(\displaystyle (x+2)^2=x^2+4x+4\) where did the \(\displaystyle 4x\) come from?
 
vissuumm said:
Hi, I'm just starting out learning this type of maths and I am confused about this answer:
(x+Δx) * (x+Δx)
= x² + 2x Δx + (Δx)²

I don't understand why it isn't:
x² + Δx² + Δx² + (Δx)²

Where does the 2x come from? Isn't x * Δx = Δx² ?

Really appreciate any help, thanks!
Click to expand...
You know that:

(a + b)2 = a2 + b2 + 2*a*b

Here you have:

a = x and

b = Δx

You can also multiply (x+Δx) * (x+Δx) out using distributive law or FOIL and get the same result.
 
Thanks for your replies!
(x+2)² = x² + 2x + 2x + 4 = x² + 4x + 4
I understand that but I don't see where the middle part 2x Δx comes from. I've been going by FOIL, therefore after multiplying x by x, I arrive at x * Δx and I don't understand why that isn't Δx², and then you have the same terms again so I thought you'd get Δx² + Δx² in place of 2x Δx.
Does my version simplify to 2x Δx ? If that's the case I can't see how.
 
tkhunny said:
Why didn't you ask the question from the beginning? Wouldn't your conclusion also mean x+Δx = x(1+Δ)? That may be a useful notation, but you should find it confusing at this moment.

Generally, though Δx indicates a process and not a multiplication.

How would you expand (x+log(x))(x+log(x))?

Alternatively, Δx means a differential. It is not meaningful if you separate the two characters.
Click to expand...

I'm not sure how I'd expand (x+log(x))(x+log(x)). I'd guess:
x² + x*log(x) + x*log(x) + (log(x))²


I'm a beginner and it's possible I'm jumping into the deep end here, so forgive me.
 
Stop telling yourself you can't do it.

That log() exercise was perfect. Now, add the two middle terms.
 
vissuumm said:
(x+2)² = x² + 2x + 2x + 4 = x² + 4x + 4
I understand that but I don't see where the middle part 2x Δx comes from. I've been going by FOIL, therefore after multiplying x by x, I arrive at x * Δx and I don't understand why that isn't Δx², and then you have the same terms again so I thought you'd get Δx² + Δx² in place of 2x Δx.
Does my version simplify to 2x Δx ? If that's the case I can't see how.
Click to expand...
This was answered in
tkhunny said:
Generally, though Δx indicates a process and not a multiplication.

It is not meaningful if you separate the two characters.
Click to expand...
The delta, Δ, is not a variable on its own; Δx must be thought of as a single symbol. (More could be said at a higher level, but this is enough.) You can't change xΔx to Δx2, because the x in Δx is not a separate item.

You may find it helpful to temporarily replace Δx with the single variable h. Then your question becomes:

(x+h) * (x+h) = x² + 2xh + h²​

Do you understand that? Then just replace h with Δx for the final answer.
 
It is simple. Δx and x are different variable. It just turns out that Δx has two parts to it, Δ and x. It is still one variable, not two variables and not a product of two variables.
 
First, you should know that [MATH]\Delta x[/MATH] should be read ''delta x'' .

This notation often refers to a diffenrence in [MATH]x[/MATH] . So that [MATH]\Delta x = (x+h)-x = h[/MATH]
If you don't like that notation you can substitute [MATH]\Delta x[/MATH] by [MATH]h[/MATH]
[MATH](x+\Delta x)^2=(x+h)^2=x^2+2xh +h^2=x^2+2x\Delta x +(\Delta x)^2[/MATH]
 
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