# Proving PatternsWatch

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#1
I have an upcoming test of the whole year's worth of maths and needed some help understanding the 'proving' part of it. I have been given some practice questions, but don't how to do one;
'Prove that (n+10)^2 - (n+5)^2 is always a multiple of 5'
0
1 year ago
#2
Is there a special way you can write the multiples of 5? Like a general term.

Then try expanding out the complicated expression, and try to simplify it into something that looks like your general term.

So as a good starting point, try to rewrite the non maths bit as a mathematical expression or (in)equality. Try to simplify the more complicated expression and then compare.
1
1 year ago
#3
Expand, simplify, take out a factor of 5, done.
0
1 year ago
#4
1) Difference of two squares
2) Done
0
1 year ago
#5
(Original post by Milli Mango)
I have an upcoming test of the whole year's worth of maths and needed some help understanding the 'proving' part of it. I have been given some practice questions, but don't how to do one;
'Prove that (n+10)^2 - (n+5)^2 is always a multiple of 5'
Technically the question as you wrote it is not correct: in order for it to be valid, it needs to specify that is an integer, as the concept of "multiple" is only applicable to integers.

Anyway, we have , where the first step comes from the difference of two squares. Now as is an integer, clearly is an integer (the reason for this is technically called closure - we would say that the set of integers is closed under addition since if you add two integers, you always get another integer; similarly the set of integers is closed under multiplication). Thus the expression is equal to times an integer, and is hence a multiple of , as required.
1
1 year ago
#6
(Original post by Milli Mango)
I have an upcoming test of the whole year's worth of maths and needed some help understanding the 'proving' part of it. I have been given some practice questions, but don't how to do one;
'Prove that (n+10)^2 - (n+5)^2 is always a multiple of 5'
You want to aim to set your working out like this:

https://ibb.co/d6QfRT
1
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