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What topic in algebra is this?

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


What topic in Algebra is it?
Reply 1
Original post by cheeriosarenice
Prove that (2n + 3)2 (2n 3)2 is a multiple of 8 for all positive integer values of n.


What topic in Algebra is it?


Well for all values of n, (2n + 3)2 (2n 3)2 = 12. Is the question correct?

Do you mean (2n+3)2(2n3)2(2n+3)^2-(2n-3)^2

If the above is the case, just expand it, you'll end up with (2n+3)2(2n3)2=8(kn)(2n+3)^2-(2n-3)^2 = 8(kn) where k will be an integer.
(edited 9 years ago)
Original post by cheeriosarenice
Prove that (2n + 3)2 (2n 3)2 is a multiple of 8 for all positive integer values of n.


What topic in Algebra is it?


Most likely Mathematical induction. Peace.
Original post by cheeriosarenice
Prove that (2n + 3)2 (2n 3)2 is a multiple of 8 for all positive integer values of n.


What topic in Algebra is it?


This is basic algebra. Expand the expression given to reveal 24n. Since 24 is a multiple of 8, then 24n is always a multiple of 8 when n is any integer.
Reply 4
Original post by WhiteGroupMaths
Most likely Mathematical induction. Peace.


Making a mountain out of a molehill
Original post by cheeriosarenice
Prove that (2n + 3)2 (2n 3)2 is a multiple of 8 for all positive integer values of n.


What topic in Algebra is it?

Ahh, good old proof by induction - oh how I loved FP1 :top: Seriously btw, it was genuinely fun and interesting - I just realised the unintended 60ft sarchasm ;D

Hope this helps :smile:
Original post by cheeriosarenice
Prove that (2n + 3)2 (2n 3)2 is a multiple of 8 for all positive integer values of n.

What topic in Algebra is it?


In most GCSE revision guides the topic would be called Algebraic PROOF
It would include questions like prove the sum of any 3 even numbers is a multiple of 6
(edited 9 years ago)
Reply 7
Original post by cheeriosarenice
Prove that (2n + 3)2 (2n 3)2 is a multiple of 8 for all positive integer values of n.


What topic in Algebra is it?


It's not a 'topic' in its own right, it's just a bit of GCSE rearrangement.
Original post by davros
It's not a 'topic' in its own right, it's just a bit of GCSE rearrangement.


I disagree ... As the previous poster said .... Algebraic proof is a topic and this is the type of question
Reply 9
Original post by TenOfThem
I disagree ... As the previous poster said .... Algebraic proof is a topic and this is the type of question


Is that actually a 'thing' in GCSE these days?

I would have said that 'proof' is just a concept that crosses all topics in mathematics rather than a specific branch of algebra. calculus etc. but then I'm not totally au fait with all these new-fangled ways of looking at things :biggrin:
Original post by davros
Is that actually a 'thing' in GCSE these days?

I would have said that 'proof' is just a concept that crosses all topics in mathematics rather than a specific branch of algebra. calculus etc. but then I'm not totally au fait with all these new-fangled ways of looking at things :biggrin:


Agreed. But
The principles of mathematical proof are superficially explored at GCSE in this type of algebraic problem, in proofs of congruent triangles and occassionally in vectors (prove ABC is a straight line).
This is a typical gcse algebraic proof question and, if the OP is searching for help with them or more practice questions, thats the topic to look for.
Original post by gdunne42
Agreed. But
The principles of mathematical proof are superficially explored at GCSE in this type of algebraic problem, in proofs of congruent triangles and occassionally in vectors (prove ABC is a straight line).
This is a typical gcse algebraic proof question and, if the OP is searching for help with them or more practice questions, thats the topic to look for.


Original post by TenOfThem
I disagree ... As the previous poster said .... Algebraic proof is a topic and this is the type of question


Yes this is a proof question, but which topic in algebra would it be classed as? My textbook doesn't have a chapter on proof, but contains all of the maths topics.
Original post by Phichi
Well for all values of n, (2n + 3)2 (2n 3)2 = 12. Is the question correct?

Do you mean (2n+3)2(2n3)2(2n+3)^2-(2n-3)^2

If the above is the case, just expand it, you'll end up with (2n+3)2(2n3)2=8(kn)(2n+3)^2-(2n-3)^2 = 8(kn) where k will be an integer.


Yeah, that's what I meant to write, but I don't get what I do next.

Original post by Doctor_Einstein
This is basic algebra. Expand the expression given to reveal 24n. Since 24 is a multiple of 8, then 24n is always a multiple of 8 when n is any integer.


How did you get 24n?
Original post by cheeriosarenice
Yes this is a proof question, but which topic in algebra would it be classed as? My textbook doesn't have a chapter on proof, but contains all of the maths topics.


As already answered, at GCSE this topic is called algebraic proof.
If you dont see this topic in the contents page, is it listed in the index?
If not there is a good starter lesson here.

https://www.youtube.com/watch?v=zCgb4z4dN60

To solve this problem you use your algebra skills with expanding brackets (or using the difference of 2 squares), simplifying by gathering like terms and factorising. If any of these skills are not second nature to you then work on that first and then move on using them to prove something is true for any positive integer value of n.
(edited 9 years ago)
Original post by Phichi
Making a mountain out of a molehill


I would have said induction too tbh!


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