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Multiplying Polynomials

Multiplying Polynomials. Applying Generic Rectangles. Creating a Generic Rectangle. WARNING: Students must have a basic understanding of Algebra Tiles to complete this tutorial. The Concept. Let’s start by using algebra tiles to multiply: (2x + 1)(x + 3). The Concept.

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Multiplying Polynomials

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  1. Multiplying Polynomials Applying Generic Rectangles

  2. Creating a Generic Rectangle WARNING: Students must have a basic understanding of Algebra Tiles to complete this tutorial.

  3. The Concept Let’s start by using algebra tiles to multiply: (2x + 1)(x + 3)

  4. The Concept Let’s start by using algebra tiles to multiply: (2x + 1) (x + 3)

  5. The Concept Let’s start by using algebra tiles to multiply: (2x + 1) (x + 3)

  6. The Concept (2x + 1) Let’s start by using algebra tiles to multiply: (2x + 1) (x + 3) (x + 3)

  7. The Concept (2x + 1) Draw in lines at every intersection to complete a rectangle: (2x + 1) (x + 3) (x + 3)

  8. The Concept (2x + 1) Remove the original tiles, and the answer remains: x (x + 3) x x 1 x x 1 x x 1

  9. The Concept (2x + 1) (2x + 1) (x + 3) x (x + 3) x x 1 x x 1 x x 1

  10. Using a Generic Rectangle Let’s do a similar example: (7x + 15)(2x + 5) For this problem using tiles would be tedious and time consuming

  11. Using a Generic Rectangle Since each parentheses has 2 terms, setup a 2 X 2 rectangle: (7x + 15)(2x + 5)

  12. Using a Generic Rectangle (7x + 15) Label the sides with each Polynomial (7x + 15) (2x + 5) (2x + 5)

  13. Using a Generic Rectangle (7x + 15) Multiply each row with each column (7x + 15) (2x + 5) (2x + 5)

  14. Using a Generic Rectangle (7x + 15) Combine like terms and write answer (7x + 15) (2x + 5) = 14x2 + 65x + 75 (2x + 5)

  15. Final Example Let’s Multiply: (3x2 – 2x + 1)(x + 3) Since there are 3 terms and 2 terms in the Parentheses, make a 3X2 rectangle

  16. Final Example (3x2 – 2x + 1) Label the sides (3x2 – 2x + 1) (x + 3) (x + 3)

  17. Final Example (3x2 – 2x + 1) Multiply each row with each column (3x2 – 2x + 1) (x + 3) 3 -2 (x + 3) 9 -6

  18. Final Example (3x2 – 2x + 1) Combine like terms and write answer (3x2 – 2x + 1) (x + 3) = 3x3 + 7x2 - 5x + 3 3 -2 (x + 3) 9 -6

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