Question

Add: \[3mn\],\[ - 5mn\],\[8mn\],\[ - 4mn\]

Answer 1

Hint: “Like terms” are terms whose variable (and their exponents such as the \[2\] in ${x^2}$) are the same.
In other words, terms that are “like” each other.
“Unlike terms” are terms which have the same variable with different exponents or different variables with the same exponents.
Example:
$7x$, $x$, $ - 2x$ are all like terms because the variable is all ‘$x$’.
They are both like terms, so you can just add or subtract them
Take another example
\[5{x^2}y + 7x{y^2} - 3xy - 4y{x^2}\]
Like term = \[5{x^2}y\] and \[ - 4y{x^2}\]
Unlike term = \[7x{y^2}\] and \[ - 3xy\]

Complete step by step solution:
We have,
$3mn$, $ - 5mn$, $8mn$, $ - 4mn$
So we have to add them, they can be written
$ = 3mn + ( - 5mn) + 8mn + ( - 4mn)$
We know that the multiplication of + and – will −.
$ = 3mn - 5mn + 8mn - 4mn$
Add same sign value together,
$ = 11mn - 9mn$
$ = 2mn$
By adding $3mn$, $ - 5mn$, $8mn$, $ - 4mn$, we get $2mn$

Note: We can add or subtract only like terms. Here is the question of why we are not using unlike terms concept over here.
The reason is simple if we see each term, which is given in the question there are two variables that contain the same power which prove that we will use the concept of Like term.

Unlike terms:
$7xy$, $7{x^2}$, $5{x^2}y$
are all unlike terms because the variable is $xy$, ${x^2}$, ${x^2}y$ not the same.
We also know to understand some point
+×+ = +
−×− = +
+×− = −
−×+ = −