Question

Add the given expression \[14x+10y-12xy-13,18-7x-10y+8xy,4xy.\]

Answer 1

Hint:Add the equations in such a way that we add the consonants having the same variable. By adding, simplify the expression.

Complete step-by-step answer:
Given are the three algebraic expressions.
\[\begin{align}
  & 14x+10y-12xy-13........(1) \\
 & 18-7x-10y+8xy........(2) \\
 & 4xy......(3) \\
\end{align}\]
An algebraic expression is built up from integers, constants, variables and algebraic operations like addition, subtraction, multiplication, division and exponentiation by an exponent.
Here, the variables used are x and y.
We need to add these 3 equations in such a way that we add the constants having the same variables.
Let us add equation (1) + equation (2) + equation (3).
\[(14x+10y-12xy-13)+(18-7x-10y+8xy)+(4xy)\]
Now let us open the brackets and arrange those terms together which have the same variables.
\[(14x-7x)+(10y-10y)+(-12xy+8xy+4xy)+(-13+18)\]
Now let us take the variables common from the brackets.
\[(14-7)x+(10-10)y+(-12+8+4)xy+(-13+18)\]
Now let’s do the algebraic addition and subtraction.
\[\begin{align}
  & =7x+0y+0xy+5 \\
 & =7x+0+0+5 \\
 & =7x+5 \\
\end{align}\]
Hence adding the three algebraic expressions gives \[7x+5\].

Note: Now we undertook the addition of the three algebraic expressions. If we were asked to subtract, then,
\[\begin{align}
  & (14x+10y-12xy-13)-(18-7x-10y+8xy)-(4xy) \\
 & =14x+10y-12xy-13-18+7x+10y-8xy-4xy \\
 & =(14x+7x)+(10y+10y)-(12xy+8xy+4xy)-(13+18) \\
 & =21x+20y-24xy-31. \\
\end{align}\]
If we subtract the expressions from the first expression, we get \[21x+20y-24xy-31.\]
But remember to be careful while solving as not to mix up variables and their signs while solving.