1/10/11 Evergreen Public Schools /24/2010 Evergreen Public Schools Notes: 5 Methods to multiply binomials Double Distribution Stacking Box FOIL Smile Vocabulary: Distributive Property polynomial monomial binomial trinomial 1/10/11 Evergreen Public Schools I can multiply polynomials and find common factors in polynomials. Give an example of a polynomial. 1/10/11 Evergreen Public Schools x(2x + 5) = 3x2x5+ 3x =6x x Remember the order of operations when simplifying simplify multiplication before simplifying addition. Multiply coefficients, and watch the exponents! 1/10/11 Evergreen Public Schools Be careful with negatives! -4x(3x - 7) = =-12x x -4x 3x - 7+ Look how minus 7 changed to plus negative 7 Simplify multiplication first! Multiply coefficients and watch the exponents be careful of negatives! ( ) Circle all the polynomials you see on in the launch. 1/10/11 Evergreen Public Schools 1/10/11 Evergreen Public Schools Factored form (x + 2)(x + 3): (x + 2) is one factor (x + 3) is the other factor A factor is anything you multiply 3 times 4 is 12: 3 and 4 are factors of 12. A = l x w length and width are factors Standard form x 2 + 5x + 6 Its what you get after multiplying factors AND simplifying Its what you get after adding all the separate areas of your rectangle AND simplifying Factored Form vs Standard Form 1/10/11 Evergreen Public Schools Factored Form = Length times Width: (x + 2) ( x + 3 ) (x + 2) Length times width always makes a rectangle. Finish your rectangle! Each rectangle is made up of lots of little rectangles. Use the dimensions to make your little rectangles. Your rectangle will have this length and width Once you have all your rectangles, count the areas to write the standard form. x2x2 xxx x x Standard Form: Standard Form (Simplified!): x 2 +5x +6 = x 2 + 5x + 6 (x + 3)(x + 2) Factored Form vs Standard Form Using Tiles 1/10/11 Evergreen Public Schools area model double distribution stacking FOIL smile 1/10/11 Evergreen Public Schools Think length times width: (2 x 1)(4 x 3) (2x 1)(4x 3) (2x (4x 3) There are 4 distinct areas in the box. 1 ) 1/10/11 Evergreen Public Schools Think length times width: (2x 1)(4x 3) (2x 1)(4x 3) (2x 1) (4x 3) Circle like terms. Simplify. 1/10/11 Evergreen Public Schools is the distributive property, except the first factor is a binomial. (2x 1) (4x 3) =(2x 1) +( ) = (2x 1)4x + (2x 1)(-3) Now distribute again. Twice! = 2x2x- 1 4x (-3) ( 4x)(-3)+ - 3 Notice the negative! (4x)+ (-1) = 8x 2 4x+ (-6x)+ 3Now combine like terms = 8x 2 10x + 3 1/10/11 Evergreen Public Schools Evergreen Public Schools Dont forget tomorrow what you learned today!!! Write what you know about Factored Form Distributive Property Area Model Double Distribution 1/10/11 Evergreen Public Schools Evergreen Public Schools Practice 7.6A Problem Numbers _______________ 1/10/11 Evergreen Public Schools Evergreen Public Schools Where are we now? I can multiply polynomials and find common factors in polynomials. 1/10/11 Evergreen Public Schools Evergreen Public Schools Read your debrief from yesterday. Use Go Round 1 Protocol. Describe each word to your group. Factored Form Distributive Property Area Model Double Distribution 1/10/11 Evergreen Public Schools Stacking works just like multiplying 34 and 97: Now, instead of integers, we multiply our binomials 34 x 97 First multiply 7 & 4. 8 Carry the 2 3 Then multiply 7 & 3 23 Then multiply 9 & 4 6 Carry the 3 Then multiply 9 & 3 31 Then ADD 3398 (2x - 1) (4x - 3) Multiply -3 & Multiply -3 and 2x -6x Multiply 4x & -1 -4x Multiply 4x & 2x 8x 2 Add like terms 8x x + 3 2 1/10/11 Evergreen Public Schools First Outside Inside Last ( )( ) 14x4x 32x2x 4x4x 2x2x 2 x (4 x ) 32x2x 2 x (-3) 14x4x -1(4 x ) 1 3 -1(-3) = 8 x 2 = -6 x = -4 x = 3 8x28x2 - 6 x - 4 x x 2 10 x + 3 Combine like terms 1/10/11 Evergreen Public Schools ( )( ) 14x4x 32x2x 4x4x 2x2x 2 x (4 x ) 32x2x 2 x (-3 x ) -1(4 x ) -1(-3) = 8 x 2 = -6 x = -4 x What does this look like to you? 8x28x2 - 6 x - 4 x = 3 8 x 2 10 x + 3 Combine like terms 1/10/11 Evergreen Public Schools Evergreen Public Schools Use 5 strategies. I will model Area Model Responsibility double distribution stacking FOIL smile 1/10/11 Evergreen Public Schools Evergreen Public Schools Which method is your favorite? Why? Tell you partner your favorite method and why its your favorite. 1/10/11 Evergreen Public Schools Evergreen Public Schools Did you hit the target? I can multiply polynomials and find common factors in polynomials. Rate your understanding of the target from 1 to 5. 5 is a bullseye! 1/10/11 Evergreen Public Schools Evergreen Public Schools Practice 7.6A Problem Numbers _______________