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.
$$\begin{array}{rl}& 14x+10y-12xy-13........(1)\\ & 18-7x-10y+8xy........(2)\\ & 4xy......(3)\end{array}$$
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.
$$\begin{array}{rl}& =7x+0y+0xy+5\\ & =7x+0+0+5\\ & =7x+5\end{array}$$
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,
$$\begin{array}{rl}& (14x+10y-12xy-13)-(18-7x-10y+8xy)-(4xy)\\ & =14x+10y-12xy-13-18+7x+10y-8xy-4xy\\ & =(14x+7x)+(10y+10y)-(12xy+8xy+4xy)-(13+18)\\ & =21x+20y-24xy-31.\end{array}$$
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.