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

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    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!
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    (Original post by blobbybill)
    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)
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    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
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    (Original post by NotNotBatman)
    \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.
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    (Original post by blobbybill)
    I don't understand what you mean.
    (4n-2) = 2(2n-1) right?
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    you could look at it as
    n* 1/2 *(4n-2)

    multiply 1/2 by (4n-2) and you get 2n-1
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    n/2(4n-2) = n((4n-2)/2) = n(2n-1)
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    (Original post by StationToStation)
    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
    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?
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    (Original post by NiamhM1801)
    n/2(4n-2) = n((4n-2)/2) = n(2n-1)
    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?
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    (Original post by blobbybill)
    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?
    You can, yeah. My method was unnecessarily long but I put it like that because I thought it'd help you understand. it would work in every instance where the numbers are multiplied by each other and not added together, I think.
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    (Original post by blobbybill)
    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?
    That's sort of what I did, I just wrote it slightly long-windedly to make it easier to understand. I don't see how it wouldn't work for other equations.
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    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
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    (Original post by Daz0101)
    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) ?
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    (Original post by blobbybill)
    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
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    (Original post by Daz0101)
    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
    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?
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    (Original post by Daz0101)
    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?
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    (Original post by blobbybill)
    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?
    You have it m8 spot on the best way to tell an expressionfrom an equation is expressions don’t usually have an equal sign and if theredo there are equal for every value of (x) example (x^2 + 4x+4) = (x+2)(x+2)that’s an expression because no matter what value you pick for x the LHS willequal the RHS or x^2 + 4x +4 is an expression because there is no RHS i.e. no equalsthat’s why you can’t multiply terms out but an equation will only ever have acouple of answers it wont be true for all values of x example 2+x=3 so this isan equation but if it was true for all values of x it would be an expression hopethis helps
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    (Original post by blobbybill)
    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?
    (4n-4) would be 2(2n-2) all you have done is take a factor of 2 out if it was (4n-1)
    you would just leave it as is as there are no common factores so the exprestion would not simplify
 
 
 
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