Polynomials with three terms are known as trinomials. We use the distributive method when we want to multiply two trinomials, when both multiplicand and multiplier are trinomial. Once u know how to multiply two binomials then it will not be hard to multiply two trinomial.

You should have to follow these two steps:

Now we are going to discuss about how to multiply trinomials. To multiply trinomials we need to follow below mentioned steps:

**Step 1:**

First you have to multiply each and every term of the second trinomial with the first term of the first trinomial and then repeat the multiplication by multiplying the second term of the second trinomial with the second term of the first trinomial and until the final term of second trinomial with the last term of first trinomial. We can apply both horizontal and vertical multiplication method.

**Step 2:**

After this, group the terms and add them.

Let’s take some example to understand the basic behind above method:

**example1:**find the multiplication of (3p^{2}+3p+1) and (3p^{2}+5p+1)

Solution: (3p^{2}+3p+1) ---->first trinomial

(3p^{2}+5p+1) ----> second trinomial

Horizontal method of multiplication-------

**Step 1: **we have to multiply the first term of first trinomial with each second trinomial term.

3p^{2}*(3p^{2}+5p+1)=9p^{4}+15p^{3}+3p^{2 }-------(a)

Multiply the second term of first trinomial with second trinomial

3p*(3p^{2}+5p+1)=9p^{3}+15p^{2}+3p ---------(b)

Multiply the last term of first trinomial with the second trinomial.

1*(3p^{2}+5p+1) = 3p^{2}+5p+1 ------------(c)

**Step 2:**

Add all the equations (a),(b),(c)

9p^{4}+15p^{3}+3p^{2}+ 9p^{3}+15p^{2}+3p+ 3p^{2}+5p+1

Group the terms having same power

9p^{4}+15p^{3}+ 9p^{3 }+3p^{2}+15p^{2}+3p^{2}+3p+5p+1

Now add the likely terms

9p^{4}+ 24p^{3 }+21p^{2}+8p+1

So the multiplication of (3p^{2}+3p+1) and (3p^{2}+5p+1) is 9p^{4}+ 24p^{3 }+21p^{2}+8p+1 (solved).