Question

Add the following expressions
\[5x - 8y + 2z,{\text{ }}3z - 4y - 2x,{\text{ }}6y - z - x\] and \[3x - 2z - 3y\]

Answer 1

Hint:
We can add or subtract the same variables by adding or subtracting their coefficients. Take the like terms together and then perform the required operation.

Complete step-by-step answer:
It is given that the expressions are \[5x - 8y + 2z,3z - 4y - 2x,6y - z - x\] and \[3x - 2z - 3y\]
Now we have to add all of these expressions.
 First we are going to add all the given expressions.
\[ \Rightarrow \left( {5x - 8y + 2z} \right) + \left( {3z - 4y - 2x} \right) + \left( {6y - z - x} \right) + \left( {3x - 2z - 3y} \right)\]
\[ \Rightarrow 5x - 8y + 2z + 3z - 4y - 2x + 6y - z - x + 3x - 2z - 3y\]
Now we are going to group the same variables.
That is, we are going to group the common terms.
\[ \Rightarrow \left( {5x - 2x - 1x + 3x} \right) + \left( { - 8y - 4y + 6y - 3y} \right) + \left( {2z + 3z - 1z - 2z} \right)\]
Now we are going to commonly take the corresponding variable in corresponding terms.
\[ \Rightarrow \left( {5 - 2 - 1 + 3} \right)x + \left( { - 8 - 4 + 6 - 3} \right)y + \left( {2 + 3 - 1 - 2} \right)z\]
Now we are going to add and subtract the numbers.
\[ \Rightarrow 5x - 9y + 2z\]
Therefore, the sum of the given expression i.e., \[5x - 8y + 2z,{\text{ }}3z - 4y - 2x,{\text{ }}6y - z - x\] and \[3x - 2z - 3y\] is \[5x - 9y + 2z\].
Additional information:
We can only add or subtract like terms.
To think of it like this we see an example. On a table we have 4 pencils and 2 pens. We cannot add the 4 pencils to the 2 pens since they are not the same kind of object.
Now we get another 3 pencils and 6 pens. Altogether we now have 7 pencils and 8 pens. We can't combine these quantities, since they are different types of objects.
Next, our sister comes in and grabs 5 pencils. We are left with 2 pencils and we still have the 8 pens.
Similarly with algebra, we can only add (or subtract) similar "objects", or those with the same letter raised to the same power.

Note:
In mathematics, addition of variables is done by adding their coefficients. Generally, addition is one of the four basic operations of arithmetic, the other three are subtraction, multiplication and division.
The development of solid understanding of addition and subtraction is essential for the development of later concepts including other arithmetical operations, calculations arising from measurements and algebra.