smallessexgirl
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Well, my sister gave me a maths question on expanding brackets and no matter what I do, I can't seem to answer it. Which I find is a bit disapointing of an A-Level maths student. The question goes as follows:

'Given that two consecutive odd numbers can be written as 2n - 1
and 2n+ I respectively, show that the difference between their
squares is 8n.'

I've tried a couple of methods and the closest I've gotten is getting an end result of -8n. Can anyone help me with this please?
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mqb2766
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(Original post by smallessexgirl)
Well, my sister gave me a maths question on expanding brackets and no matter what I do, I can't seem to answer it. Which I find is a bit disapointing of an A-Level maths student. The question goes as follows:

'Given that two consecutive odd numbers can be written as 2n - 1
and 2n+ I respectively, show that the difference between their
squares is 8n.'

I've tried a couple of methods and the closest I've gotten is getting an end result of -8n. Can anyone help me with this please?
I guess you;ve done
(2n-1)^2 - (2n+1)^2
to get -8n?

Just swap the order of subtraction
(2n+1)^2 - (2n-1)^2 = ...
Last edited by mqb2766; 3 weeks ago
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heccyeah
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(Original post by smallessexgirl)
Well, my sister gave me a maths question on expanding brackets and no matter what I do, I can't seem to answer it. Which I find is a bit disapointing of an A-Level maths student. The question goes as follows:

'Given that two consecutive odd numbers can be written as 2n - 1
and 2n+ I respectively, show that the difference between their
squares is 8n.'

I've tried a couple of methods and the closest I've gotten is getting an end result of -8n. Can anyone help me with this please?
-8n is still a difference of 8n between them
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smallessexgirl
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(Original post by mqb2766)
I guess you;ve done
(2n-1)^2 - (2n+1)^2
to get -8n?

Just swap the order of subtraction
(2n+1)^2 - (2n-1)^2 = ...
Even if I switch them around, I'll get get the same answer due to the signs. Originally, I wrote:
4n^2 - 4n + 1 - 4n^2 - 4n - 1
= -8n


Switiching them around, I get:
- 4n^2 - 4n - 1 + 4n^2 - 4n + 1

Either way it would be -8n and the question asks for +8n...

Thank you, tho!
Last edited by smallessexgirl; 3 weeks ago
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smallessexgirl
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(Original post by heccyeah)
-8n is still a difference of 8n between them
I suppose you could argue that but the question asks for +8n, not -8n. Since a difference of -8n wouold lead you in the opposite direction to a difference of +8n...

We'll see though what her teacher says, thank you tho!
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heccyeah
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lol
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mqb2766
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(Original post by smallessexgirl)
Even if I switch them around, I'll get get the same answer due to the signs. Originally, I wrote:
4n^2 - 4n + 1 - 4n^2 - 4n - 1
= -8n


Switiching them around, I get:
- 4n^2 - 4n - 1 + 4n^2 - 4n + 1

Either way it would be -8n and the question asks for +8n...

Thank you, tho!
(2n+1)^2 - (2n-1)^2
When you expand the first term (2n+1)^2, its impossible for any of the terms to be negative.
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smallessexgirl
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(Original post by heccyeah)
(2n+1)^2 - (2n-1)^2

= (4n^2+4n+1) - (4n^2-4n+1)
= 4n - - 4n
= 4n + 4n
= 8n
Ohh, that makes more sense!! Thank you so much!!
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smallessexgirl
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(Original post by mqb2766)
(2n+1)^2 - (2n-1)^2
When you expand the first term (2n+1)^2, its impossible for any of the terms to be negative.
(2n-1)^2
= 4n^2 - 4n + 1

-(4n^2 - 4n + 1)
= -4n^2 + 4n - 1


This was the logic I used but this may be wrong-
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Muttley79
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(Original post by heccyeah)
(2n+1)^2 - (2n-1)^2
PLEASE don't break forum rules but giving answers
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mqb2766
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(Original post by smallessexgirl)
(2n-1)^2
= 4n^2 - 4n + 1

-(4n^2 - 4n + 1)
= -4n^2 + 4n - 1



This was the logic I used but this may be wrong-
Sure that is correct for the second term, but the first term gives all positive parts. Just add the two terms together then and you get the result.
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smallessexgirl
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(Original post by mqb2766)
Sure that is correct for the second term, but the first term gives all positive parts. Just add the two terms together then and you get the result.
Yeah, that makes more sense, thank you!!
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0ptics
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(Original post by smallessexgirl)
'Given that two consecutive odd numbers can be written as 2n - 1
and 2n+ I respectively, show that the difference between their
squares is 8n.'
Since the word in bold is used, I’m pretty sure that what you did initially is correct. I mean the method used to get -8n.
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