Section 9-3 Multiplying Binomials SPI 12D: multiply two polynomials with each factor having no more than two terms Objectives: Multiply binomials by modeling.

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Section 9-3 Multiplying Binomials SPI 12D: multiply two polynomials with each factor having no more than two terms Objectives: Multiply binomials by modeling Multiply binomials using the Foil method Multiply a trinomial and a binomial Use the distributive property When multiplying like bases, add exponents Combine like terms – when combining do not change the degree (exponent); just add the coefficients Write polynomial in standard form (highest degree first)

x + 4 2x + 3 Use an area model to multiply two binomials Model the problem (2x + 3)(x + 4) x 1 Legend x2x2 x2x2 xxxx x x x xxxx x(x + 4) = 2x 2 + 8x 3(x + 4) = 3x x 2 + 8x 3x x 2 +11x + 12

Methods used to Multiply Binomials Simplify (4x + 2)(3x – 6). The product is 12x 2 – 18x – 12. Last (2)(–6)+ Outer (4x)(–6) + Inner (2)(3x) + 24x 6x12 –+– = 12x 2 18x – 12 – First = (4x)(3x) (4x + 2)(3x – 6) Three Methods 1. Foil Method 2. Vertical Method 3. Box (Punnett Square) Method FOIL Method

Methods used to Multiply Binomials Simplify (4x + 2)(3x – 6). Vertical Method 4x + 2 3x – 6 x -24x – 12 12x 2 + 6x 12x 2 – 18x – 12 Multiply each term by -6 Multiply each term by 3x

Genetics Punnett Squares are diagrams used by scientists to help them to figure out how inherited traits (characteristics) will be distributed. F f f f FfFf FfFf ff We will use something like a Punnett Square as a method to multiply polynomials!! Methods used to Multiply Binomials

1 st Create a box 4 th Combine like terms 5 th Write in Standard Form 2 nd Insert terms Box (Punnett Square) Method Methods used to Multiply Binomials Simplify (4x + 2)(3x – 6) using the box method. 3 rd Multiply terms 4x + 2 3x x 2 6x -24x-12 12x 2 – 18x – 12

Find the area of the shaded region. Simplify. area of outer rectangle = (3x + 2)(2x – 1) area of hole = x(x + 3) area of shaded region = area of outer rectangle – area of hole = (3x + 2)(2x – 1) – x(x + 3)Substitute. = 6x 2 – 3x + 4x – 2 –x 2 – 3x Use FOIL to simplify (3x + 2) (2x – 1) and the Distributive Property to simplify x(x + 3). = 6x 2 – x 2 – 3x + 4x – 3x – 2Group like terms. = 5x 2 – 2x – 2Simplify. Applying Multiplication of Polynomials

Practice 1. Simplify the product using the FOIL method. (x + 2)(x + 5) 2. Simplify the product using the vertical method. (r + 6)(r – 4) 3. Simplify using the box method. (- 7 + p)(8 + p) 4.Use any method to simplify the products (a – 4)(a 2 – 2a + 1) 5. Simplify (2x + 2) 2 x 2 + 7x + 10 r 2 + 2r – 24 p 2 + p – 56 a 3 - 6a 2 + 9a -4 4x 2 + 8x + 4