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Chapter 9 Section 4

Chapter 9 Section 4. Multiplying Binomials. Directions: Use the model to find the product of (x + 2) (x -1) Step 1 Put the x + 2 and the x – 1 outside the box as shown. x -1 x 2. Note: x – 1 = x + (-1). Step 2.

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Chapter 9 Section 4

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  1. Chapter 9 Section 4 Multiplying Binomials

  2. Directions: Use the model to find the product of (x + 2) (x -1) Step 1 Put the x + 2 and the x – 1 outside the box as shown. x -1 x 2 Note: x – 1 = x + (-1).

  3. Step 2 Use the Distributive Property to Multiply x by x – 1 and place the products inside the boxes. x -1 x

  4. Step 3 Use the Distributive Property to multiply 2 by x – 1 and place the products inside the boxes. x -1 x 2

  5. Step 4 Find the sum of the terms inside the boxes: x -1 x 2 x2 – 1x + 2x - 2 = x2 + 1x - 2 or x2 + x - 2

  6. Multiplying Binomials (x + 2)(x + 1) x 1 x(x + 1) = x(x) + x(1) x = x2 + 1x 2 2(x + 1) = 2(x) + x(1) = 2x + 2 So, x2 + 1x + 2x + 2 = x2 + 3x + 2 Combine like terms

  7. Your Turn Directions: Use the box model to find each product. (x + 2)(x + 3) x 3 x 2 x2 + 2x + 3x + 6 = x2 + 5x + 6

  8. Try Another (x + 3)(x + 4) x 4 x 3 x2 + 4x + 3x + 12 = x2 + 7x + 12

  9. Try Again (2x + 1)(x + 1) x 1 2x 1 2x2 + 2x + 1x + 1 = 2x2 + 3x + 1

  10. Try another with a minus sign!! (x – 2)(x + 1) x 1 x -2 x2 + 1x -2x -2 = x2 -1x -2 or x2 -x -2

  11. Try this problem with 2 minus signs!! (x – 3)(x – 2) x -2 x -3 x2 – 2x – 3x + 6 = x2 – 5x + 6

  12. Practice makes perfect!!! (x – 1)(x + 1) x 1 x -1 x2 + 1x – 1x – 1 = x2 – 1

  13. FOIL Method Without using the box method you can multiply binomials by using the FOIL method. F – The first terms. O – The outside terms. I – The inside terms. L – The last terms.

  14. Example 1 Combine like terms Find each product. (y + 4)(y + 6) (y + 4)(y + 6) = First Terms y(y) = y2 Outside Terms y(6) = 6y Inside Terms 4(y) = 4y Last Terms 4(6) = 24 y2 + 6y + 4y + 24 = y2 + 10y + 24

  15. Example 2 (2x – 3)(2x + 2) (2x - 3)(2x + 2) = First Terms 2x(2x) = 4x2 Outside Terms 2x(2) = 4x Inside Terms -3(2x) = -6x Last Terms -3(2) = -6 Combine like terms 4x2 + 4x – 6x -6 = 4x2 -2x -6

  16. Example 3 (3a – b)(2a + 4b) (3a – b)(2a + 4b) = First Terms 3a(2a) = 6a2 Outside Terms 3a(4b) = 12ab Inside Terms -b(2a) = -2ab Last Terms -b(4b) = -4b2 Combine like terms. 6a2 + 12ab -2ab -4b2 = 6a2 + 10ab -4b2

  17. Example 4 Find the product of x2 – 4 and x – 3. (x2 – 4)(x – 3) (x2 – 4)(x – 3)= First Terms x2(x) = x3 Outside Terms x2(3) = 3x2 Inside Terms -4(x) = -4x Last Terms -4(-3) = 12 x3 + 3x2 -4x + 12 = x3 + 3x2 -4x + 12 There are no like terms.

  18. Your Turn Find the product of x – 2 and x2 + 3. (x – 2)(x2 + 3) (x – 2)(x2 + 3)= First Terms x(x2) = x3 Outside Terms x(3) = 3x Inside Terms -2(x2) = -2x2 Last Terms -2(+3) = -6 x3 - 2x2 + 3x - 6 There are no like terms. Notice I put the terms in descending order.

  19. Video For FOIL • FOIL

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