Adding, Subtracting, Multiplying Polynomials

Polynomials can be added or subtracted following a very simple rule: only coefficients of like terms can be added or subtracted. Like or similar terms are defined as those having the same variables raised to the same power.

For example, the terms are similar but the terms are not similar because they don't have the same variable, regardless of them having the same power.

Two terms are multiplied (assuming they have the same variable) by multiplying the coefficients and in a separate process, the variables are multiplied following the properties of the exponentials:

For example, the following terms are multiplied as shown:

To multiply a monomial by a polynomial, we apply the distributive property of multiplication:

Multiplying polynomials is a repetition of the procedure mentioned above. Let's multiply the given polynomials:

We first multiply the first term of the left polynomial by both terms of the right polynomial. Then, we multiply the second term by both terms:

Operating:

Since no similar terms are found, we just rearrange the polynomial in descending order: