The polynomials is a part of algebra in which operations like division, multiplication, addition and subtraction are performed. Multiplying Polynomials Calculator will help us to multiply the any two polynomials. Multiplying polynomial enables us to model and solve real life problems.  
To multiply the polynomials, you need to keep few simple general rules in your mind:
When a polynomial with 'n' terms are multiplied with another polynomial of 'm' terms then 
  1. The each term in the first polynomial should be multiplied with the each other terms of second polynomial. 
  2. After multiplying, the product should be equal to the number of terms in first factor to the second factor.
  3. Group them to get the proper answer. 
  4. Don't miss any terms and once you get the product collect and simplify the like terms.
Now lets learn multiplication of polynomial step by step.

Step1: Every term in the first polynomial has to be multiplied with every term in the second.

For example: (x2 - 3x + 2)$\times$(4x3 + 5x2 + 6x)

Now every term in second expression is multiplied with x2:

x2(4x3 + 5x2 + 6x) = 4x5 + 5x4 + 6x3

Step 2: Next multiply -3x with every term in second expression:

-3x(4x3 + 5x2 + 6x) = -12x4 - 15x3 - 18x2

Step 3: In same way multiply 2 with every term in second expression

2(4x3 + 5x2 + 6x) = 8x3 + 10x2 + 12x

Step 4: Take all the nine terms in right hand side and add them by combing the like terms.

4x5 + 5x4 + 6x3 - 12x4 - 15x3 - 18x2 + 8x3 + 10x2 + 12x = 4x5 + x4 (5 - 12) + x3 (6 - 15 + 8)  + x2 (-18 + 10) + 12x

= 4x5 - 7x4 - 8x2 + 12x

Answer: 4x5 - 7x4 -  x3 - 8x2 + 12x.

In simple words you just need to distribute each term of the polynomial with one another.