Question

Add the expressions $14x+10y-12xy-13,18-7x-10y+8xy,4xy$.

Answer 1

Hint: For solving this question you should know about the addition of variables with multiplicand. We will solve this question by putting terms and expressions as normal addition and then add the same variable terms and subtract them also. So, it will be like a normal addition and subtraction.

Complete step-by-step solution:
According to our question we have to add $14x+10y-12xy-13,18-7x-10y+8xy,4xy$. So, if we want to add these then we have to put some variable terms near to each other and we will perform the operation. And if we see an example for it, then it will be clear to us.
Example 1: Add $4{{x}^{2}}+3{{x}^{3}}+2x-6{{y}^{2}},8{{x}^{2}}-6{{y}^{3}},-4{{x}^{3}}+3{{x}^{2}}-8{{y}^{3}}$.
If we want to add them then,
$\Rightarrow 4{{x}^{2}}+3{{x}^{3}}+2x-6{{y}^{2}}+8{{x}^{2}}-6{{y}^{3}}-4{{x}^{3}}+3{{x}^{2}}-8{{y}^{3}}$
Now take the same variable with each other, so,
$\begin{align}
  & \Rightarrow 4{{x}^{2}}+8{{x}^{2}}+3{{x}^{2}}+3{{x}^{3}}+2x-6{{y}^{2}}-8{{y}^{3}}-6{{y}^{3}}-4{{x}^{3}} \\
 & \Rightarrow 15{{x}^{2}}+\left( -1{{x}^{3}} \right)+2x-14{{y}^{3}}-6{{y}^{2}} \\
 & \Rightarrow 15{{x}^{2}}+2x-{{x}^{3}}-14{{y}^{3}}-6{{y}^{2}} \\
\end{align}$
So, if we see our question then:
$=14x+10y-12xy-13+18-7x-10y+8xy+4xy$
Now, if we take the same variables terms with each other, then, we get,
 $=14x-7x+10y-10y-12xy+8xy+4xy-13+18$
And if we solve this, then we will get,
$\begin{align}
  & =7x+0y+0xy+5 \\
 & =7x+5 \\
\end{align}$
So, here we get the solution as $7x+5$.

Note: During solving this question you should be careful about the terms of x and y because all these will decide this question. If any one will be wrong then your entire question will be wrong and always make equations in order they are given, otherwise the equations will not be correct and the answer will be wrong and if we want to solve big powered questions, then too it will be the same. Then we will put all the same variables with the same power near to each other and then we perform our task of addition and submission whatever is given in the question.