Solve Multiplying Trinomials

In Algebra trinomial is a polynomial having three terms .otherwise it consisting of three monomial. For an example.

8x + 5y + 3z having x, y z variable

4t + 6s2 + 3y3 Here t, s, y is a variable

5ts + 9t + 6s with t, s variables

Here we are going to study about how to solve multiply a trinomial and its example problems.
Solve example problems for multiplying trinomial

Example: 1

Multiplying trinomial with binomial

Solve (x2+2x+3) (3x+3)

Solution:

First we have to take 3x multiply with trinomials

3x3+6x2+9x

Next we take a 3

3x2+6x+9

Now combine the like terms

3x3+6x2+3x2+9x+6x+9

3x3+10x2+15x+9

This is the multiplying answer.

Example: 2

Multiplying trinomial with another trinomial

Solve (x2 +3x+3) (2x2 +6x+4)

Solution:

Here there are two trinomial is given

First we have to multiply the x2  term to the other trinomial we get

2x (2+2) +6x (2+1) + 4x2

= 2x4+6x3+4x2

Next we take the 3x term we get

3*2x(1+2)+ 3*6x2+12x

= 6x3+18x2+12x

Finally we take a constant term 3

= 6x2+18x+12

Now we combine all the terms we get

= 2x4+6x3+4x2 + 6x3+18x2+12x + 6x2+18x+12

Combine the like term x3

6x3+6x3 = 12 x3

Combine x2 term

= 4x2+18x2+6x2

= 28x2

Combine x term

12x+18x=30x

Therefore the final answer is

2x4+12x3+28x2+30x+12

Multiplying trinomial with same trinomial

Example: 3

Solve (x2+3x+2) (x2+3x+2)

Solution:

Now we have to expand the polynomial

Take x2 and multiply with all the terms we get

X4+3x3+2x2

Similarly take 3x and multiply with all the term we get

3x3+9x2+6x

Finally take constant 2 multiply with all the term we get

2x2+6x+4

Now we combine all the term

X4 +3x3 + 2x2 + 3x3 + 9x2 + 6x + 2x2 + 6x + 4

Combine the like terms we get

3x3+3x3= 6x3

Combine the x2 terms

2x2+2x2+9x2 = 13x2

Similarly combine the x term

6x+6x=12x

Finally constant 4

Combine all the terms

x4+6x3+13x2+12x+4

This is the multiplying answer for the given two trinomials.