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Binomials

Multiplying and Factoring Binomials . 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

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Binomials

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  1. Multiplying and Factoring Binomials Binomials

  2. 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

  3. 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.

  4. 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

  5. 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

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

  7. 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.

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