How does n/2(4n-2) simplify to give n(2n-1)?

How does n/2(4n-2) simplify to give n(2n-1)?

i thought that to cancel out the n/2, you multiply it by 2, which would give n(8n-4)?
Am I just derping? is it as simple as n(8n-4), which is then simplified to n(2n-1)? Is that possible?
Thanks!

$\frac{n}{2}(4n-2) =\frac{(n)(4n-2)}{2}$ ?

Factorise a factor of 2 in (4n-2), (4n-2) =2(2n-1)

I don't understand what you mean.

Ah no, you can't multiply it because it's not a normal equation! You can think about it this way:

n/2(4n-2) = (n(4n-2))/2 = n x (4n-2)/2 = n x (4n/2 - 2/2) = n x (2n-1) = n(2n-1)

Hope this made it clearer

n/2(4n-2) = n((4n-2)/2) = n(2n-1)

Thanks. I understand it now, but that seems like a very long winded method.

Are there any other simpler methods?

For example, can you just divide the bracket contents of (4n-2) by 2, so that both sides are divided by two? That works in this instance, would it work in every instance though?

Thanks! In addition to this method, are there any other even simpler ways?#

For example, can you just divide the bracket contents of (4n-2) by 2, so that both sides are divided by two and then the divided by two would cancel out? That works in this instance, would it work in every instance though? Is that a valid method too, or is it just that it happens to work in this instance?

this is an expression not an equation so you can’t multiplyout anything the only thing you can do to an expression is simply if by taking outfactors so just look at the bracket and ask yourself what common factors canyou take out and its a 2 so the 2s cancel and give you the expression you wantof n(2n-1) j

When you say the twos cancel out, do you mean get rid of the 2 from n/2, and then also divide the bracket by 2 (from 4n-2 to give 2n-1) ?

yes, that’s it you have it just remember in expressions you can’t divide or multiply terms out you can cancel and simplify that’s it so dont say divide by2 say take a factor of 2 out if you think like that when you see expressionsyou automatically know what to do if you confuse the two by the way you’rethinking about it you will make silly mistakes I used to do that so never say dividefor an expression then you never get the 2 confused hope that helps

yes, that’s it you have it just remember in expressions you can’t divide or multiply terms out you can cancel and simplify that’s it so dont say divide by2 say take a factor of 2 out if you think like that when you see expressionsyou automatically know what to do if you confuse the two by the way you’rethinking about it you will make silly mistakes I used to do that so never say dividefor an expression then you never get the 2 confused hope that helps

OHH, do you mean that by taking out a factor of something, eg, x in the equation 4x -4, you mean that you only take out x where there is an x available, so you don't divide by x?

With this expression i just described ^^, taking out a factor of x would result in 4 -4, whereas if you divided by x, it would go to 4 - 4/x? Am I right in thinking this? Is this what you mean?

i dont get it, I dont understand the difference between dividing and multiplying, and removing/adding factors of a number?
If you take out a factor of two, you divide everything by two don't you (because you take a ? if not, how does it work? Whats the difference by taking out a factor of two and dividing by two?