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

Last updated date: 11th Aug 2024
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Hint:Add the equations in such a way that we add the consonants having the same variable. By adding, simplify the expression.

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.