Question

Subtract:
\[3xy + 5yz - 7zx\] from \[5xy - 2yz - 2zx + 10xyz\]

Answer 1

Hint:
Here we need to find the difference between the two expressions. For that, we will subtract the first expression from the second expression. We will subtract the like terms of the first expression from the like terms of the second expression. After subtracting all the like terms, we will get the required simplified value of the difference between the given two mathematical expressions.

Complete step by step solution:
Here we need to find the difference of the two mathematical expressions and the given two mathematical expressions are \[3xy + 5yz - 7zx\] and \[5xy - 2yz - 2zx + 10xyz\]
For that, we will subtract the first expression from the second expression.
On subtracting the first expression from the second expression, we get
Difference \[ = 5xy - 2yz - 2zx + 10xyz - \left( {3xy + 5yz - 7zx} \right)\]
Now, we will open the bracket by multiplying the number -1 to each term.
\[ \Rightarrow \] Difference\[ = 5xy - 2yz - 2zx + 10xyz + \left( { - 1} \right) \times 3xy + \left( { - 1} \right) \times 5yz - \left( { - 1} \right) \times 7zx\]
On multiplying the terms, we get
\[ \Rightarrow \] Difference \[ = 5xy - 2yz - 2zx + 10xyz - 3xy - 5yz + 7zx\]
Now, we will add or subtract the like terms in the expression.
\[ \Rightarrow \] Difference \[ = 2xy - 7yz + 5zx + 10xyz\]
We can see that there are no more like terms, so we can’t simplify the expression further.

Therefore, the required value of the difference of the two expressions i.e. \[3xy + 5yz - 7zx\] and \[5xy - 2yz - 2zx + 10xyz\] is equal to \[2xy - 7yz + 5zx + 10xyz\].

Note:
Adding or subtracting the like terms means to add or subtract the coefficient of the terms whose variables are same or the terms in which the power of all the variables are same.
We can’t simplify the expression \[2xy - 7yz + 5zx + 10xyz\] further as there are no like terms left to get simplified further. Like terms in an algebraic expression are the terms which have the same variables but the coefficient may or may not be the same.