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 **

- The each term in the first polynomial should be multiplied with the each other terms of second polynomial.

- After multiplying, the product should be equal to the number of terms in first factor to the second factor.

- Group them to get the proper answer.

- 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: (x

^{2} - 3x + 2)$\times$(4x

^{3} + 5x

^{2} + 6x)

Now every term in second expression is multiplied with x

^{2}:

x

^{2}(4x

^{3} + 5x

^{2} + 6x) = 4x

^{5} + 5x

^{4} + 6x

^{3}
**Step 2:** Next multiply -3x with every term in second expression:

-3x(4x

^{3} + 5x

^{2} + 6x) = -12x

^{4 }- 15x

^{3 }- 18x

^{2}**Step 3:** In same way multiply 2 with every term in second expression

2(4x

^{3} + 5x

^{2 }+ 6x) = 8x

^{3 }+ 10x

^{2 }+ 12x

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

4x

^{5} + 5x

^{4 }+ 6x

^{3 }- 12x

^{4 }- 15x

^{3 }- 18x

^{2 }+ 8x

^{3 }+ 10x

^{2 }+ 12x = 4x

^{5} + x

^{4 }(5 - 12) + x

^{3 }(6 - 15 + 8)

^{ }+ x

^{2 }(-18 + 10)

^{}+ 12x

= 4x

^{5} - 7x

^{4 }- 8x

^{2 }+ 12x

Answer: 4x^{5} - 7x^{4 }- x^{3 }- 8x^{2 }+ 12x.

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