Answer

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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.

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.

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.

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