A major understanding about polynomials in general is the concept of "like terms". Two monomials are like terms provided the same variables AND same exponents are in each term. See the following table for examples:
| Examples of Like Terms | Non-examples |
|---|---|
| \(3x^2\) and \(-5x^2\), same variable \(x\) and same exponent \(2\). | \(x+y\) NOT like terms, different variables used. |
| \(14a^3b^5\) and \(-8.3a^3b^5\), same variables \(a,b\), \(a\) has an exponent of \(3\) in BOTH terms, likewise, \(b\) has an exponent of \(5\) in BOTH terms. | \(5d^4\), \(-6d\) and \(4\) NOT like terms, different exponents on each monomial. |
Now that an understanding of what like terms are, addition can formally be defined. To add polynomials, you add together the like terms by adding ONLY the coefficients of the monomials. The exponents stay the same in the like terms. Subtraction follows the same way, with the exception being to distribute through the second polynomial that subtraction first, then add together the new like terms. The following video will show an example of each.