Math Is Fun Forum

evene

Member

Registered: 2015-10-18

Posts: 272

Proving the following factorizations

How would you prove this:

I'm confused on how you would prove them...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Proving the following factorizations

Hi;

For the first one, I have seen a couple of demonstrations of these before:

http://math.stackexchange.com/questions … lify-an-bn

See Mawhrin-Skel's post. If his algebra ( I have not checked, you now have the means to check anyone's work... ) is correct then it is short and sweet. Another, explanation is given here...

http://math.stackexchange.com/questions … ctor-an-bn

Sweet use of a generating function.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,624

Re: Proving the following factorizations

hi evene

For number one the right hand side looks more complicated so I tried to make RHS into the LHS.

That gave me the clue to do it the other way round, ie. LHS => RHS.

Proof:

Collect all the + terms together and factorise out an 'a'.  Then all the - terms and factorise out a 'b'.

I think you can do the others similarly.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Proving the following factorizations

First ensure remainder is zero and then use long division.

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