How to Expand Trinomials

Trinomials have three terms and appear in all levels of math curriculum.
••• Digital Vision./Digital Vision/Getty Images

With binomials, students expand the terms with the common Foil method. The process for this method involves multiplying the first terms, then the outside terms, the inside terms, and finally the last terms. However, the Foil method is useless for expanding trinomials because although you can multiply the first terms, the inside and last terms overlap, and if you multiply per the Foil method, you remove one of the factors necessary to come up with the correct solution. In addition, the products of the terms are quite lengthy and the chances of mathematical errors are great.

    Examine the trinomial (x + 3)(x + 4)(x + 5).

    Multiply the first two binomials using the distributive property. (x) x (x) = x^2, (x) x (4) = 4x, (3) x (x) = 3x and (3) x (4) = 12. You should have a polynomial that reads x^2 + 4x + 3x + 12.

    Combine like terms: x^2 + (4x + 3x) + 12 = x^2 + 7x + 12.

    Multiply the new trinomial by the last binomial from the original problem with the distributive property: (x + 5)(x^2 + 7x + 12). (x) x (x^2) = x^3, (x) x (7x) = 7x^2, (x) x (12) = 12x, (5) x (x^2) = 5x^2, (5) x (7x) = 35x and (5) x (12) = 60. You should have a polynomial that reads x^3 + 7x^2 + 12x + 5x^2 + 35x + 60.

    Combine like terms: x^3 + (7x^2 + 5x^2) + (12x + 35x) + 60 = x^3 + 12x^2 + 47x + 60.

Related Articles

How to Factor Polynomials in Factor Four Terms
Polynomials: Adding, Subtracting, Dividing & Multiplying
How to Solve Polynomial Equations
How to Do Multiplying & Factoring Polynomials
How to Solve Rational Expression Equations
How to Factorise in Math
What are the Rules For Multiplying Fractions?
How to Factor Trinomials, Binomials & Polynomials
How to Factor Polynomials of Degree 3
Associative Properties of Math for Kids
How to Check Multiplication
How to Simplify Monomials
How to Factor Polynomials for Beginners
How to Help With Polynomials
How to Multiply Monomials
How to Factor a Perfect Cube
How to Solve Cubic Equations
How to Factor Polynomials With 4 Terms
The Foil Method With Fractions
How to Calculate Volume of Polynomials

Dont Go!

We Have More Great Sciencing Articles!