Factorisation X to the 5 plus Y to the 5

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Jignesh77

Junior Member
Joined
Dec 8, 2020
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66
Good morning everyone,

I am a matured student and love learning maths in my spare time. I would be very grateful if you can show me and explain the steps to solve or factorise the following:
X to the 5 plus Y to the 5.
Sorry I don't know how to write the expression properly.
Thank you!
 
Jignesh77 said:
Good morning everyone,

I am a matured student and love learning maths in my spare time. I would be very grateful if you can show me and explain the steps to solve or factorise the following:
X to the 5 plus Y to the 5.
Sorry I don't know how to write the expression properly.
Thank you!
Click to expand...
Is this what you mean [imath]x^5+y^5?[/imath]
 
In ordinary typing you can type x^5+y^5,
Using the tags [ imath] x^5+y^5[/imath] (without the space alter [) we get [imath] x^5+y^5[/imath]
Here is a factorization: SEE HERE
 
pka said:
In ordinary typing you can type x^5+y^5,
Using the tags [ imath] x^5+y^5[/imath] (without the space alter [) we get [imath] x^5+y^5[/imath]
Here is a factorization: SEE HERE
Click to expand...
What happened to learning by DISCOVERY?
 
I would have started by asking @Jignesh77 if they could think of a possible value of [imath]x[/imath] that satisfies [imath]x^5+y^5=0[/imath]. But then I personally don't see any difference between a young student and a mature student.
 
Jignesh77 said:
What about x=1 and y = -1?
Click to expand...
That's correct, and it's good thinking. Can you leave y as a variable, and write x in terms of y? x=<something in terms of y>

EDIT: In other words, what value of x (written in terms of y) will always be a solution to [imath]x^5+y^5=0[/imath].
EXAMPLE: [imath]x=y^2[/imath] would NOT be correct because [imath]\left(y^2\right)^5 + y^5 \ne 0[/imath] (for all values of y)
 
Last edited:
Subhotosh Khan said:
Can you divide ( x5+y5\displaystyle x^5 + y^5 x5+y5) by (x + y) using one of the methods learned for polynomial division?

You may want to Google the term "polynomial division" and get some background information
Click to expand...
Can you divide ( x^5+y^5) by (x + y) using one of the methods learned for polynomial division?
 
Let me try and see if I can follow the steps. Thank you for being so kind and helpful.
 
I tried couple of times but eventually got it. Thank you!

youtube]NItvj0FqvsA

The video by Dr. Masi on YouTube about this type of examples really helped me.

Thank you all for your time and help!

youtube]NItvj0FqvsA
 
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