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August 11th, 2018, 11:53 AM  #1 
Newbie Joined: Jun 2018 From: Jordan Posts: 14 Thanks: 0  Some questions related to variables and operations
Hi. I got several algebraic questions and I don't really want them to remain a gap for me. First one is about substituting variables / expressions; Say that we have $\displaystyle (xy)^3=4x$. If I decide to substitute the expression $\displaystyle xy$ with the variable $\displaystyle n$, which is the new correct form of the utter expression? 1 $\displaystyle n^3 = 4x $ 2 $\displaystyle n^3 = 4n/y$ (assuming $\displaystyle x = n/y$) 3 Both The next question is, If I substitute a variable with an expression, do I have to do it everywhere? For example; Say that $\displaystyle y = 3x$ and $\displaystyle g * \sqrt{y} = 2y$ Can it be $\displaystyle g*\sqrt{y} = 6x$ ? Another question ; If I were to multiply / divide a fraction by a value that has many forms, can I use different forms for certain purposes? Say I want to multiply $\displaystyle \frac{x}{y}$ with 1, but also $\displaystyle \sin^2(x) + \cos^2(y) = 1$. is this correct? $\displaystyle \frac{x}{y} = \frac {x(\sin^2(x)+\cos^2(x))}{y} $ Last question ; is the above case possible when it comes to equations too? For example, assume that $\displaystyle g+c = 3 $ and I have the equation: $\displaystyle 3x^2 = y $ If I multiply both sides by 3, but in 2 different forms $\displaystyle 9x^2 = y(g+c) $ is this correct? ^ Thanks in advance. Last edited by skipjack; August 15th, 2018 at 03:33 AM. 
August 11th, 2018, 12:22 PM  #2  
Senior Member Joined: Sep 2015 From: USA Posts: 2,123 Thanks: 1102  Quote:
Quote:
Can you? Sure, equality is equality. If two elements are equal, you can freely substitute one for another. Quote:
Quote:
Last edited by skipjack; August 15th, 2018 at 03:38 AM.  
August 14th, 2018, 01:03 AM  #3 
Newbie Joined: Jun 2018 From: Jordan Posts: 14 Thanks: 0 
Thanks!

August 14th, 2018, 04:31 AM  #4  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,315 Thanks: 935  Quote:
 
August 15th, 2018, 01:39 AM  #5 
Newbie Joined: Jun 2018 From: Jordan Posts: 14 Thanks: 0  Yep I know that it would give the same answer but my question wasn't whether it would be the same in terms of value or not. All I wanted to know is whether is it permissible to do such operations or not. (For e.g: having a new variable in terms of 2 subvariables and then using it along with another subvariable in the same expression such as my first example)


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