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C4: Binomial expansion, quick question!

Hi,

How is 4+2x=2(1+12x)12\sqrt {4+2x} = 2(1+\frac{1}{2}x)^\frac{1}{2}
This was a question on the MEI C4 June 2005 paper.
Just wondering how they've got to this step in the mark scheme as I thought it would be 4+2x=4(1+12x)12\sqrt {4+2x} = 4(1+\frac{1}{2}x)^\frac{1}{2}
Thanks in advance!
Reply 1
Avatar for gdunne42
gdunne42
21
When you factorise out the 4 you also have to apply the power of 1/2 to it

(4 + 2x)^1/2

[4(1 + 1/2x)]^1/2

Posted from TSR Mobile
(edited 10 years ago)
Original post by Kiran96
Hi,

How is 4+2x=2(1+12x)12\sqrt {4+2x} = 2(1+\frac{1}{2}x)^\frac{1}{2}
This was a question on the MEI C4 June 2005 paper.
Just wondering how they've got to this step in the mark scheme as I thought it would be 4+2x=4(1+12x)12\sqrt {4+2x} = 4(1+\frac{1}{2}x)^\frac{1}{2}
Thanks in advance!

square root of (4+2x) can be written as (4+2x)^1/2, then you take a factor of 4 so its (4(1+0.5x))^1/2= 2(1+0.5x)^1/2
Reply 3
Avatar for Kiran96
Kiran96
OP
Original post by gdunne42
When you factorise out the 4 you also have to apply the power of 1/2 to it

(4 + 2x)^1/2

[4(1 + 1/2x)]^1/2

Posted from TSR Mobile



Original post by BasharAssad
square root of (4+2x) can be written as (4+2x)^1/2, then you take a factor of 4 so its (4(1+0.5x))^1/2= 2(1+0.5x)^1/2


Ah I see, I've got to be careful with the brackets then. Thank you both for your help!

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