Adding and Subtracting Polynomials

This video shows how to simplify and add and subtract polynomial expressions. The key is to group like terms and carry through the signs when adding and subtracting.

Adding and Subtracting Polynomials

Adding and Subtracting Polynomials

Here, we’re asked to simplify a pair of polynomial expressions. Now the keys here are going to be to group like terms, and to carry through the signs when adding or subtracting. In the first example, we have x squared plus 4x, plus 2, plus x squared, minus 3x, minus 4.

We’re going to group our like terms together. We have (from the first expression) x squared plus (from the second expression) x squared, plus 4x, plus negative 3x (so, we’ll have minus 3x), plus 2, plus negative 4 (so, minus 4). Now we already have our like terms grouped, so we’re going to add each of these separately.

X squared plus x squared is 2x squared, plus 4x minus 3x is going to be plus x, and plus 2 minus 4 is going to be minus 2. This is the simplified form of that expression. In the second example, we have a minus sign here, so we have to be careful to carry this minus sign through when we try to include the second and third terms of the second expression.

We’ll start here, we have an x squared, and then (from the second expression) minus x squared, plus 3 x, minus negative x (so that’s a plus x), minus 5, minus plus 3, (so minus 3). Once again we have our like terms already grouped, so we’ll go ahead and add them separately.

X squared minus x squared is going to be 0, 3x plus x is going to be 4x, and minus 5 minus 3 is going to be a minus 8. What we have here, this 0 can just go away, and we have 4x minus 8, or 4 times x, minus 2.