Multiplying Trinomials

An Algebraic expression in the form axn is called a monomial in x, where a is a known number, x is a variable and n is a non-negative integer. The coefficient of yn and n has a number, the degree of the monomial. For example, 7x3 is a monomial in x of degree 3 and 7 is the coefficient of x3.When we have  2 monomial in the polynomial function it is known as a binomial , similarly sum of three monomial is called a trinomial. For example, 2x5 – 3x2 + 3 is a trinomial. we can perform various operations like addition, subtraction, multiplication and division. Now we are going to see multiplying trinomials.

Methords of multiplying trinomials:

We can multiply the trinomials by using the distributive method, in that there are two methods followed one is Horizontal method, and the other one is vertical method.

Horizontal method:

This horizontal method is one of the distributive methods. This is used for multiplying the trinomials in horizontal form and simplify them.

Vertical method:

This vertical method is one of the distributive methods. This is used for multiplying the trinomials in vertical form and simplify them.

These are illustrated below with examples

Example for multiplying trinomials:

Example 1:

Using the vertical method and multiply the trinomials

(a + 5) (a2 + 7a + 8)

Solution:

Given, (a + 5) (a2 + 7a + 8)

Using vertical method, we multiply the given trinomial

a2 + 7a + 8

a + 5

a3 + 7a2 + 8a                multiply the trinomial a2 +7a + 8 from the second binomial term a.

5a2  + 35a + 40    multiply the trinomial a2 +7a + 8 from the second binomial term + 8

a3 + 12a2 + 43a + 40       (Combine like terms then we get result)

Solution to the given trinomials is a3 + 12a2 + 43a + 40.

Example 2:

Using the horizontal method and multiply the trinomials

(a + 6) ( a2 + 12a + 23)

Solution:

Given

(a + 6) ( a2 + 12a + 23)

Using horizontal method, we multiply the given trinomial

(a + 6) ( a2 + 12a + 23)

Multiply the trinomial a2 + 12a + 23 from the second binomial term a.

(a2 + 12a +23) × (a)

a3 + 12a2 + 23a

Multiply the trinomial a2 + 12a + 23 from the second binomial term 6.

(a2 + 12a + 23) × 6

6a2 + 72a + 138

Group like terms

a3 + 12a2 + 23a + 6a2 + 72a + 138

a3 + 12a2 + 6a2 + 23a + 72a + 138



Combine like terms

a3 + 18a2 + 95a + 138

Solution to the given trinomials is a3 + 18a2 + 95a + 138