Step-by-step explanation:
This is simple. Like terms are those whose variable is the same raised to the same power. It doesn't matter if the coefficient is different, but the variables must be equal.
Example 1:
[tex]x+2x=?[/tex]
x has an invisible 1 in front of it, and the other x is accompanied by a 2. Both have an x, raised to the first power, therefore, they're like terms. Add the coefficients (2 and 1) and leave the same variable (x)
[tex]x+2x=3x[/tex]
Example 2:
[tex]4x^2-3x^2=?[/tex]
Both coefficients have a variable x raised to the second power, therefore, they're like terms. Subtract the coefficients and leave the same variable raised to the same power.
[tex]4x^2-3x^2=x^2[/tex]
1 is already implied to be there, that's why I don't put it.
Example 3:
[tex]4x+3+x^2-x=?[/tex]
It can be challenging to see which terms are like terms when they're not in a specific order. In this case, it's easier if we simply group like terms separately. However, I can only see 2 like terms.
[tex](4x-x)+x^2+3[/tex]
I grouped them so that it's easy for me to solve the operation.
[tex]3x+x^2+3[/tex]
Always try to order the equation from the variable with the highest exponent to the one with the lowest exponent.
[tex]x^2+3x+3[/tex]
This expression has no more like terms. Why? [tex]x^2[/tex] has a power of 2, [tex]3x[/tex] has an x to the power of 1, and [tex]3[/tex] has no variables. Therefore, none of them are like to one another.
