Simplifying Expressions
By S Taylor
You probably know that if you have an expression like
you cannot add those terms to simplify it in any way. That’s because one term in a constant (the 4) and the other term has a variable (the x). We say that these are not like terms and cannot be combined.
However, if you have something like
,
we say those are like terms because they have the same variable raised to the same power. In this case, we can combine the like terms to get
.
Notice that to be considered like terms, not only do you have to have the same variable, but it also has to be to the same power. So we cannot combine
because even though the variable is the same, the powers are not. But we can combine
because we have the same variable raised to the same power.
Things become a little more complicated if we have more than one variable in a term. In that case, all variables and powers must match up exactly.
The expression
cannot be simplified. However,
is possible.
In some cases, you may have to perform other simplification before you can combine like terms. For example, to simplify
you will need to use the distributive property first and then combine any like terms:
The main thing to keep in mind is to eliminate any parentheses that might be in the problem and then combine like terms if possible. Remember that it may not be possible to do any simplification. Not all expressions can be expressed in a more reduced form.
you cannot add those terms to simplify it in any way. That’s because one term in a constant (the 4) and the other term has a variable (the x). We say that these are not like terms and cannot be combined.
However, if you have something like
,
we say those are like terms because they have the same variable raised to the same power. In this case, we can combine the like terms to get
.
Notice that to be considered like terms, not only do you have to have the same variable, but it also has to be to the same power. So we cannot combine
because even though the variable is the same, the powers are not. But we can combine
because we have the same variable raised to the same power.
Things become a little more complicated if we have more than one variable in a term. In that case, all variables and powers must match up exactly.
The expression
cannot be simplified. However,
is possible.
In some cases, you may have to perform other simplification before you can combine like terms. For example, to simplify
you will need to use the distributive property first and then combine any like terms:
The main thing to keep in mind is to eliminate any parentheses that might be in the problem and then combine like terms if possible. Remember that it may not be possible to do any simplification. Not all expressions can be expressed in a more reduced form.
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