Multiplying Binomials using Algebra tiles and Rectangle Diagrams Polynomials Lesson 2 Multiplying Binomials using Algebra tiles and Rectangle Diagrams

Todays Objectives Students will be able to demonstrate an understanding of the multiplication of polynomial expressions, including: Multiply two polynomials symbolically, and combine like terms in the product Generalize and explain a strategy for multiplication of polynomials Express a polynomial as a product of its factors

Multiplying Binomials Today we will look at two different strategies for multiplying binomials: Algebra Tiles Rectangle diagrams

Multiplying with Algebra Tiles x+3 Step 1: Draw two dimensions, write polynomials beside them x + 5

Multiplying with Algebra Tiles x+3 Step 1: Draw two dimensions, write polynomials beside them Step 2: Represent the two polynomials x + 5

Multiplying with Algebra Tiles x+3 Step 1: Draw two dimensions, write polynomials beside them Step 2: Represent the two polynomials Step 3: Draw the tiles x + 5

Multiplying with Algebra Tiles x+3 Step 1: Draw two dimensions, write polynomials beside them Step 2: Represent the two polynomials Step 3: Draw the tiles Step 4: Color the tiles x + 5

Multiplying with Algebra Tiles x+3 Step 1: Draw two dimensions, write polynomials beside them Step 2: Represent the two polynomials Step 3: Draw the tiles Step 4: Color the tiles Step 5: Get the result x + 5 (x+3)(x+5) = x2 + 5x + 3x + 15 = x2 + 8x + 15

Multiplying with Algebra Tiles x+2 Step 1: Draw two dimensions, write polynomials beside them 2x-3

Multiplying with Algebra Tiles x+2 Step 1: Draw two dimensions, write polynomials beside them Step 2: Represent the two polynomials 2x-3

Multiplying with Algebra Tiles x+2 Step 1: Draw two dimensions, write polynomials beside them Step 2: Represent polynomials Step 3: Draw the tiles 2x-3

Multiplying with Algebra Tiles x+2 Step 1: Draw two dimensions, write polynomials beside them Step 2: Represent polynomials Step 3: Draw the tiles Step 4: Color the tiles 2x-3

Multiplying with Algebra Tiles x+2 Step 1: Draw two dimensions, write polynomials beside them Step 2: Represent polynomials Step 3: Draw the tiles Step 4: Color the tiles Step 5: Get the result 2x-3 (2x-3)(x+2) = 2x2 + 4x – 3x – 6 = 2x2 + x - 6

If the numbers are big…

Rectangle Diagrams x2 -x 1 2x2 -x -6x 3

Multiplying with Rectangle Diagrams 12x + 32 23 + 13x

Multiplying with Rectangle Diagrams 12x + 32 156x 2 416x 276x 736 23 + 13x

Multiplying with Rectangle Diagrams 12x + 32 156x 2 416x 276x 736 23 + 13x (12x+32)(13x+23) = 156x2 + 416x + 276x + 736 = 156x2 + 692x + 736

Ascending and Descending Order Some questions will ask you to write your answer in ascending or descending order. Ascending order: write each term in order of INCREASING exponent value. Example: 5 – 3x + 2x2 + 4x3 Descending order: write each term in order of DECREASING exponent value. Example: 4x3 + 2x2 – 3x + 5

Review Quiz (x+7) (x+4) (x+6) (x-7) (x+47)(x+26) (2x+3) (3x-7) (31x-67) (49x+72) x2 + 11x + 28 x2 – x - 42 x2 + 73x + 1222 6x2 - 5x - 21 1519x2 - 1051x - 4824