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Multiplying Polynomials

Multiplying Polynomials. How Do you find the area of a rectangle? . How would you find the area of this house lot?. x ² . 2x. 5x. 10. x ² + 2x + 5x + 10 = x ² + 7x + 10. Find The Area of the Lot. 3x. 5. 2x. 6x ² . 10x. 8. 24x. 40. 6x ² + 24x + 10x + 40 =

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Multiplying Polynomials

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  1. Multiplying Polynomials

  2. How Do you find the area of a rectangle? • How would you find the area of this house lot? x² 2x 5x 10 x² + 2x + 5x + 10 = x² + 7x + 10

  3. Find The Area of the Lot. 3x 5 2x 6x² 10x 8 24x 40 6x² + 24x + 10x + 40 = 6x² + 34x + 40

  4. Example 1: Find the product of (3x + 5) (5x – 10) 3x +5 5x 25x 15x² -10 -30x -50 15x² - 30x + 25x - 50 = 15x² - 5x - 50

  5. (3x + 5) (5x – 10) Using The FoIL Method*only used when multiplying 2 binomials F – First O- Outer I – Inner L - Last

  6. (3x + 5) (5x – 10) • First: first number times the first number (3x +5) (5x–10) 3x(5x) = 15x² • Outer: Outer number times the outer number (3x +5) (5x–10) 3x(–10) = -30x

  7. (3x + 5) (5x – 10) • Inner: inner number times the inner number (3x +5) (5x–10) 5(5x) = 25x • Last: Last number times the last number (3x +5) (5x–10) 5(–10) = -50

  8. F: 15x² • O: -30x • I : 25x • L: -50 15x²- 30x + 25x - 50 = 15x² - 5x - 50

  9. Example 2: Find the Product of (4x – 9)(x – 11) = 4x² -53x +99 Example 3: Find the Product of (5x – 4)(5x + 4) = 25x² - 16 Example 4: Find the Product of (3x + 9)(3x +9) = 9x² + 54x + 81

  10. Example 5: Find the Product of (2x² – 2x + 12)(-5x – 1) -5x -1 2x² -10x³ -2x² 10x² 2x -2x -60x 12 -12 = -10x³ +8x² -58x -12

  11. (2x² – 2x + 12)(-5x – 1) 2x²(-5x) + 2x²(-1) -2x(-5x) -2x(-1) +12(-5x) +12(-1) = -10x³ -2x² +10x² + 2x -60x -12 = -10x³ + 8x² - 58x - 12

  12. Find the product of:A) (xy)²b) (x + y)²c) (x – y) ²d) (X +y) (x – y) =x²y² =x² + 2xy +y² =x² - 2xy +y² =x² - y²

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