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 Do Multiplying & Factoring Polynomials
Polynomials: Adding, Subtracting, Dividing & Multiplying
How to Factor Polynomials in Factor Four Terms
How to Solve Rational Expression Equations
How to Calculate Volume of Polynomials
How to Solve Polynomial Equations
How to Factor Polynomials of Degree 3
How to Divide Polynomials By Monomials
How to Factor Polynomials & Trinomials
How to Factor Binomial Cubes
How to Factor Third Power Polynomials
How to Solve Cubic Equations
How to Factorise in Math
How to Simplify Monomials
How to Factor a Perfect Cube
How to Factor Higher Exponents
How to Factor Trinomials, Binomials & Polynomials
How to Factorise a Quadratic Expression
How to Do Exponents Outside of the Parenthesis
Tricks for Factoring Quadratic Equations

Dont Go!

We Have More Great Sciencing Articles!