Multiplying and Factoring Binomials

Multiplying Binomials  In multiplying binomials, such as (3x - 2)(4x + 5), you might use a generic rectangle.  Make sure that you multiply each term in the correct box. Don’t forget the negatives!  12x² - 8x + 15x – 10  Combine like terms  12x² + 7x – 10

Factoring Binomials  Diamond Problems can be used to help factor easier quadratics like x² + 6x + 8.  Look at the 8, what two numbers multiply together to get 8.  Look at the 6, do those numbers also add up to 6?  If not, try another set of numbers that multiply together to get 8.  When you are successful, write the answers as shown above in the example.

Factoring and Multiplying Binomials  Factoring and Multiplying are opposites. They undo each other. If you multiply a binomial, you can then factor that equation and you will end up with the same answer you started with. X² + 3x - 10

Multiplying Binomials by FOIL Method.  Another approach to multiplying binomials is to use the mnemonic ‘F.O.I.L.’ F.O.I.L. is an acronym for First, Outside, Inside, Last:  (3x - 2)(4x + 5) F. multiply the FIRST terms of each binomial (3x)(4x) = 12x² O. multiply the OUTSIDE terms (3x)(5) = 15x I. multiply the INSIDE terms (-2)(4x) = -8x L. multiply the LAST terms of each binomial (-2)(5) = -10

FOIL Method Continued After FOIL-ing, combine like terms. 12x² + 15x – 8x – 10 12x² + 7x – 10

Factoring Binomials With Coefficients Other Than 1.  We can modify the diamond method slightly to factor problems that are a little different in that they no longer have a “1” as the coefficient of x2. For example, factor:  Another problem: 5x2 - 13x + 6. Note that the upper value in the diamond is the product of 5 and 6.