Multiplication Involving Trinomials Topic Index | Algebra Index | Regents Exam Prep Center

Multiplying a Binomial and a Trinomial

 Put the "distributive method" of multiplication to work.  Multiply each term from the binomial times each term of the trinomial.  You can do this by using either a horizontal method or a vertical method. Note:  FOIL will not work in this problem.

Horizontal Method:

 (x + 3)(x² + 2x + 4) = x³ + 2x² + 4x + 3x² + 6x + 12 = x³ + 2x² + 3x² + 4x + 6x + 12  Group like terms. = x³ + 5x² + 10x + 12     Combine like terms.

Vertical Method:

 x² + 2x + 4 x + 3 x³ + 2x² + 4x
 3x² + 6x + 12 Line up like terms. x³ + 5x² + 10x + 12 Add like terms.

Cubing a Binomial

 Expand:   (x + 3)³ If you take your time, this problem is really very simple.    All you need to do is multiply twice.  Multiply (x + 3) times (x + 3), and then  multiply that answer by (x + 3).  Simple!
 (x + 3)³ = (x + 3)(x + 3)(x + 3) = (x² + 3x + 3x + 9)(x + 3)     the first multiplication is done = (x + 3) (x² + 6x + 9)       combine like terms and switch order = x³ + 6x² + 9x + 3x² + 18x + 27   multiply again = x³ + 9x² + 27x + 27    combine like terms

The "distributive method" of multiplication was used in this problem.
Note:  FOIL will not work for the second multiplication in this problem.

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