Sioned D. 13 Plus  English tutor, 11 Plus English tutor, 13 Plus  Mat...
£18 - £25 /hr

Sioned D.

Degree: Law (Bachelors) - University College London University

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About me

Hi! My name is Sioned, and I'm a final year law student at University College London (UCL). I can help with admissions tests for Law, general application guidance for applying to Law at University or for the dreaded (!) LNAT. I have also studied Maths, English, Music, History and Biology to A level so I can help GCSE students in need of help with those subjects.  Get in touch! 

Subjects offered

SubjectLevelMy prices
Biology GCSE £18 /hr
Maths GCSE £18 /hr
English 13 Plus £18 /hr
Maths 13 Plus £18 /hr
English 11 Plus £18 /hr
Maths 11 Plus £18 /hr
.LNAT. Uni Admissions Test £25 /hr

Qualifications

QualificationLevelGrade
EnglishA-LevelA*
HistoryA-LevelA*
BiologyA-LevelA
MusicA-LevelA
Mathematics (AS)A-LevelA
Welsh Baccalaureate A-LevelA
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Questions Sioned has answered

Prove that (2n+3)^2-(2n-3)^2 is a multiple of 8 for positive integer values of n

To prove that (2n+3)2-(2n-3)2 is a multiple of 8 we are going to deal with the first bracket and then the second bracket.  When a bracket has 2 next to it, this means that you multiplying the bracket, by the bracket itself.  So, we are going to put them side by side, like this: (2n  +3) (2n ...

To prove that (2n+3)2-(2n-3)is a multiple of 8 we are going to deal with the first bracket and then the second bracket. 

When a bracket has next to it, this means that you multiplying the bracket, by the bracket itself. 

So, we are going to put them side by side, like this:

(2n  +3) (2n + 3) 

To multiply everything in the first bracket, by everything in the second bracket, we can use a multiplication square, or, we can use this easy way to remember how to multiply out the bracket. 

F O I L 

This stands for: 

First 

Outside 

Inside 

Last 

This means that you are going to multiply the first two terms in the brackets by each other

2n x 2n =4n2

Then you are going to multiply the outside terms in the brackets by each other. 

2n x 3 = 6n

Then you multiply the inside terms by each other, 

2n x 3 = 6n

Then you multiply the last two terms in each bracket by each other. 

3 x 3 = 9 (be careful of the negatives here)

Putting all of this together, we get:

4n2 + 6n + 6n +9

Well done, first bit complete!

*****************************************

Then you deal with the second bit 

- (2n-3)2

So, be very careful here. There is a negative sign in front of the bracket. To avoid confusion later on, let's put a big bracket around it. 

- [(2n-3)2]

everything we do in this section is going to be inside that big square bracket...

-[(2n-3)(2n-3)]

following FOIL again and keeping that big bracket in place...

-[4n-6n -6n +9]

make sure you watch out for that (-3 x -3) which makes a +9

and then, because we have that big bracket around this equation, we are going to multiply it out. 

so, 

-4n2 + 12n -9

********************************************************

So putting the first bit and the second bit together (and watching out for those negatives!), we get...

4n+12n +9 - 4n2 + 12n -9

now we are going to tidy that up a little bit, collecting the like terms....

4n2 -4n=0

and +9 -9 =0

So, we are just left with 24n 

If you didn't know what an integer was... it means WHOLE NUMBER. So to show that the integer is a multiple of 8, we are going to show that 

to get 24n you can take out a factor of 8...

and this leaves you with 8(3n). 

this shows that if you take out a factor of 8 you still get a whole number in front of n, which answers the question!

see more

6 days ago

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