Messing with Dimensions

I have a question for you all:

Why can't we subtract cm from cm^2 ?

It is confusing why schools told us to subtract like terms and not unlike terms. Well cm^2 is cm*cm so it composes of cm.

I think it is related to algebra like y^2-y where y^2 is y times y but we can't do anything with y because y^2=y times y and not subtraction. But y^2-y gives you some answer.

This is also related to imaginary numbers. i^2=-1. But -1-i=something confusing. So I keep my roots on imaginary than algebra.

can anyone help me clear my confusion for the above problem.

Note by Mohmmad Farhan
1 year, 2 months ago

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If yy is any integer or real number then y2y=y(y1)y^2 - y = y(y - 1). It is the product of two consecutive integers or any two real numbers yy and y1y - 1 so you will definitely get answer.

Ram Mohith - 1 year, 2 months ago

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But say for example we have 4cm^2 - 8cm

Mohmmad Farhan - 1 year, 2 months ago

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It just of the form : AreaPerimeterArea - Perimeter.

Ram Mohith - 1 year, 2 months ago

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@Ram Mohith oh

Mohmmad Farhan - 1 year, 2 months ago

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@Ram Mohith Is it possible to get a more simplified result

Mohmmad Farhan - 1 year, 2 months ago

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@Mohmmad Farhan Not possible. If it is mentioned that cmcm is not any unit and it is just a constant then the simplified form will be 4cm(cm2)4cm(cm - 2)

Ram Mohith - 1 year, 2 months ago

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@Ram Mohith oh

Mohmmad Farhan - 1 year, 2 months ago

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We can cancel out or add any two like terms if and only if both the like terms are of the same degree.

Ex:5y3y=2yEx : 5y - 3y = 2y. Here 5y5y and 3y3y are of same degree that is 11 so you can subtract them or you can add them .

But what about (x3x)(x^3 - x) ?

Solution : You cannot subtract them nor you can add them. The reason is that the first xx is of the degree 33 where as the second xx is of the degree 11.

What about y3y2+5y+2y+3y^3 - y^2 + 5y + 2y + 3 ?

Solution : You cannot add or subtract y3y^3 and y2y^2 because there of different degree : 33 and 22 respectively. Coming to 5y5y and 2y2y they are of same degree 11 so they add up to become 7y7y. Now again y3,y2,7y and 3y^3,y^2,7y ~and~3 cannot be added because they are of different degrees 3,2,1,03,2,1,0 respectively.

Coming to x3y3x^3 - y^3 what will you say about this ?

Solution : Nothing can be done as they are unlike terms.

Mohammad Farhan you should be strong in these basic fundamentals for you to solve further higher questions.

Ram Mohith - 1 year, 2 months ago

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OK

Mohmmad Farhan - 1 year, 2 months ago

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Coming to the first part of the note your query itself is in an undetermined form . You should note that cm,cm2,cm3,m3,g,kg,etccm,cm^2,cm^3,m^3,g,kg,etc are all units and they can neither be added nor subtracted nor multiplied nor any operation can be done. Don't be confused.

Ram Mohith - 1 year, 2 months ago

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Lets go to the prime powers relationship

Mohmmad Farhan - 1 year, 2 months ago

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I have to award my mentor. What would you want

Mohmmad Farhan - 1 year, 2 months ago

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