Like Terms
Like terms are terms that share the exact same variable part, with each variable raised to the same exponent. The numerical coefficients can differ. For instance, 3ab and 5ab are like terms.
A practical example
These two terms are considered like terms because they contain the same variables, each raised to the same power:
$$ 3a^2b^3 \quad 5a^2b^3 $$
In contrast, the following terms are not like terms - while they include the same variables, the exponents are different:
$$ 3a^5b^4 \quad 5a^2b^3 $$
Likewise, these terms are not like terms either, as they involve different variables altogether:
$$ 3c^2b^3 \quad 5a^2b^3 $$
Adding and subtracting like terms
Adding like terms
When you add two like terms, the result is another like term with the same variable part and a coefficient equal to the sum of the original coefficients.
To add like terms, simply add the numerical coefficients while keeping the variable part unchanged.
Example
Let’s add the following like terms:
$$ 3a^2b + 5a^2b $$
We apply the distributive property to factor out the common variable part (a2b):
$$ (3 + 5) \cdot a^2b $$
Then, we carry out the addition:
$$ 8a^2b $$
Subtracting like terms
Subtracting like terms works the same way: you subtract the coefficients and keep the variable part unchanged.
Example
Let’s subtract the following like terms:
$$ 7a^2b - 5a^2b $$
Again, we factor out the common variable part using the distributive property:
$$ (7 - 5) \cdot a^2b $$
And we perform the subtraction:
$$ 2a^2b $$
And so on.
