It is very easy to understand. This is what we all learn in high schools but we will review this to make sure that you know this concept.
Let's suppose that we have two polynomials.
Is it possible to add these polynomials? Yes, it is certainly possible but what is the methodology to add two polynomials.
Step 1: First step is to find terms in both the polynomials having same variables. For example, in the above polynomials, we have terms and having same variable . Also, we have terms and both having variables and .
Step 2: From the terms chosen in step 1, select the ones which are having same value of exponents. For example, terms and both have their exponent equal to 2. Terms and both have their exponent equal to 5. Similarly, the terms and have same values of exponents for variables and .
Step 3: We add the coefficients of the terms which are having same variables and exponents. For example, we chose and in step 2. So, we just add their coefficients to add these terms. And, the result is .
Similarly, we add terms and and the result of their addition is obtained by just adding their coefficients. Rest of the term remain as it is. So, the result is
After understanding this whole process, are you able to quickly add two given polynomials? Let's try this.
(Note that terms and 5 remain as they are.)
How do we subtract polynomials?
Subtracting is not very different from adding polynomials. We again deal with the coefficients of terms having same variables and exponents.
(We are just subtracting the coefficients.)
Similarly, we can add multiple polynomials and can subtract multiple polynomials from one polynomial.