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
6 days, 10 hours ago

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I have to award my mentor. What would you want

Mohmmad Farhan - 3 days, 10 hours ago

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Lets go to the prime powers relationship

Mohmmad Farhan - 3 days, 10 hours 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 \(cm,cm^2,cm^3,m^3,g,kg,etc\) 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 - 3 days, 10 hours 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.

\(Ex : 5y - 3y = 2y\). Here \(5y\) and \(3y\) are of same degree that is \(1\) so you can subtract them or you can add them .

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

Solution : You cannot subtract them nor you can add them. The reason is that the first \(x\) is of the degree \(3\) where as the second \(x\) is of the degree \(1\).

What about \(y^3 - y^2 + 5y + 2y + 3\) ?

Solution : You cannot add or subtract \(y^3\) and \(y^2\) because there of different degree : \(3\) and \(2\) respectively. Coming to \(5y\) and \(2y\) they are of same degree \(1\) so they add up to become \(7y\). Now again \(y^3,y^2,7y ~and~3\) cannot be added because they are of different degrees \(3,2,1,0\) respectively.

Coming to \(x^3 - y^3\) 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 - 3 days, 10 hours ago

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OK

Mohmmad Farhan - 3 days, 10 hours ago

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

Ram Mohith - 3 days, 10 hours ago

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

Mohmmad Farhan - 3 days, 10 hours ago

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It just of the form : \(Area - Perimeter\).

Ram Mohith - 3 days, 10 hours ago

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

Mohmmad Farhan - 3 days, 10 hours ago

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

Ram Mohith - 3 days, 10 hours ago

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@Ram Mohith oh

Mohmmad Farhan - 3 days, 10 hours ago

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@Ram Mohith oh

Mohmmad Farhan - 3 days, 10 hours ago

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