# 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.

6 days, 10 hours ago

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I have to award my mentor. What would you want

- 3 days, 10 hours ago

Lets go to the prime powers relationship

- 3 days, 10 hours ago

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.

- 3 days, 10 hours ago

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.

- 3 days, 10 hours ago

OK

- 3 days, 10 hours ago

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.

- 3 days, 10 hours ago

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

- 3 days, 10 hours ago

It just of the form : $$Area - Perimeter$$.

- 3 days, 10 hours ago

Is it possible to get a more simplified result

- 3 days, 10 hours ago

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

- 3 days, 10 hours ago

oh

- 3 days, 10 hours ago

oh

- 3 days, 10 hours ago