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.
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 Seriously btw, it was genuinely fun and interesting - I just realised the unintended 60ft sarchasm ;D
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
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
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
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.
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.
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.
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.
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.
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.