Question

If $A = 2{y^2} + 3x - {x^2},B = 3{x^2} - {y^2},C = 5{x^2} - 3xy$ then find $A + B$

Answer 1

Hint:
For solving this type of question we just have to write the equation in order and line up the corresponding variables and then we just add the same variables with each other and we will get to the answer easily.

Complete step by step solution:
First of all we will write the equation, which is given as $A = 2{y^2} + 3x - {x^2},B = 3{x^2} - {y^2},C = 5{x^2} - 3xy$
Now we have to find $A + B$
So for this, we will add both of the equations. By substituting the values, we get
$ \Rightarrow (2{y^2} + 3x - {x^2}) + (3{x^2} - {y^2})$
Now on arranging the equation in order, which will like the highest power will at first position then on decreasing it, so we get
$ \Rightarrow (2{y^2} - {x^2} + 3x) + (3{x^2} - {y^2})$
Now on removing the braces, and adding the equation, we get
$ \Rightarrow 2{y^2} - {x^2} + 3x + 3{x^2} - {y^2}$
Therefore, on rearranging the above equation, which will like the highest power will at first position then on decreasing it, so we get
$ \Rightarrow 2{y^2} - {y^2} - {x^2} + 3{x^2} + 3x$
Now on solving. We get
$ \Rightarrow {y^2} + 2{x^2} + 3x$

Hence, the value $A + B$ will be ${y^2} + 2{x^2} + 3x$.

Additional information:
While solving it we should always keep the like terms together and then solve accordingly, whether we have to add or subtract. But if we have to find the values of the variables then we have to eliminate one of the variables then we can solve it easily and find the values of both the variables if the question is of two variables.

Note:
To tackle this type of problem the terms with factors, generally we rework the terms with basic factors and add them independently, in a couple of questions where we need to demonstrate the R.H.S. side we need to remember the terms on the opposite side too to acquire the ideal outcome.