# expansion of (4-5x)^1/2

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I know that the genral formular for binomial expansion with rational powers is: (1+x)^n= 1+nx+n(n-1)/2! and so on.

However I dont under stand how the first and second terms of the expansion are 2 and 5/4x. Surely they should be 4 and 5/2x as n in this case is 1/2 and x is 5x. What am i doing wrong here?

However I dont under stand how the first and second terms of the expansion are 2 and 5/4x. Surely they should be 4 and 5/2x as n in this case is 1/2 and x is 5x. What am i doing wrong here?

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#2

Can you show the working and I can highlight the error ? I’m assuming you may have taken the 4 out of the brackets but not taken the power with it….?

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#3

(Original post by

I know that the genral formular for binomial expansion with rational powers is: (1+x)^n= 1+nx+n(n-1)/2! and so on.

However I dont under stand how the first and second terms of the expansion are 2 and 5/4x. Surely they should be 4 and 5/2x as n in this case is 1/2 and x is 5x. What am i doing wrong here?

**ImBadAt**)I know that the genral formular for binomial expansion with rational powers is: (1+x)^n= 1+nx+n(n-1)/2! and so on.

However I dont under stand how the first and second terms of the expansion are 2 and 5/4x. Surely they should be 4 and 5/2x as n in this case is 1/2 and x is 5x. What am i doing wrong here?

Last edited by RogerOxon; 4 weeks ago

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(Original post by

Can you show the working and I can highlight the error ? I’m assuming you may have taken the 4 out of the brackets but not taken the power with it….?

**Maths Fan**)Can you show the working and I can highlight the error ? I’m assuming you may have taken the 4 out of the brackets but not taken the power with it….?

so should it be 4^1/2 as the first term giving 2. But then how is 5/4x made?

Last edited by ImBadAt; 4 weeks ago

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#5

So from your working I can see you’ve not manipulated the bracket correctly at the start.

(4-5x)^1/2 , needs to be changed so it’s in the required form to continue if that makes sense?

(4-5x)^1/2 , needs to be changed so it’s in the required form to continue if that makes sense?

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(Original post by

So from your working I can see you’ve not manipulated the bracket correctly at the start.

(4-5x)^1/2 , needs to be changed so it’s in the required form to continue if that makes sey

**Maths Fan**)So from your working I can see you’ve not manipulated the bracket correctly at the start.

(4-5x)^1/2 , needs to be changed so it’s in the required form to continue if that makes sey

Last edited by ImBadAt; 4 weeks ago

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#8

(Original post by

Yes that makes sence, Thankyou. I needed to factor out ther 4 right?

**ImBadAt**)Yes that makes sence, Thankyou. I needed to factor out ther 4 right?

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(Original post by

Don't forget the power too ...

**Muttley79**)Don't forget the power too ...

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#10

(Original post by

ok so i factor out 4^1/2 which is 2. I then do the expansion of (1+5/2x)^1/2. And im assuming that at the end i would multiply all the terms by 4^1/2?

**ImBadAt**)ok so i factor out 4^1/2 which is 2. I then do the expansion of (1+5/2x)^1/2. And im assuming that at the end i would multiply all the terms by 4^1/2?

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