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Do Now:

Learn how to multiply polynomials using the Box Method with step-by-step examples and practice problems. Master this versatile technique and simplify complex expressions effortlessly.

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Do Now:

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  1. Do Now: What’s the formula for area, again? x - 5 What is the area of the shaded region? 2x - 9

  2. The 2nd method is the Box Method. This method works for every problem! Here’s how you do it: (3x – 5)(5x + 2) Draw a box. Write a polynomial on the top & side of a box. It does not matter where. This will be modeled in the next problem along with FOIL.

  3. 3) Multiply (3x - 5)(5x + 2) 15x2 First terms: Outer terms: Inner terms: Last terms: Combine like terms. 15x2 - 19x – 10 +6x -25x 15x2 -25x -10 +6x -10 You have 2 techniques. Pick the one you like the best!

  4. First terms: Outer terms: Inner terms: Last terms: Combine like terms. 21p2 – 34p + 8 4) Multiply (7p - 2)(3p - 4) 21p2 -28p -6p 21p2 -6p +8 -28p +8

  5. Multiply (y + 4)(y – 3) • y2 + y – 12 • y2 – y – 12 • y2 + 7y – 12 • y2 – 7y – 12 • y2 + y + 12 • y2 – y + 12 • y2 + 7y + 12 • y2 – 7y + 12

  6. Multiply (2a – 3b)(2a + 4b) • 4a2 + 14ab – 12b2 • 4a2 – 14ab – 12b2 • 4a2 + 8ab – 6ba – 12b2 • 4a2 + 2ab – 12b2 • 4a2 – 2ab – 12b2

  7. So, what if you have a binomial x trinomial? Please copy: (x + 3)(x² + 2x + 4)

  8. Horizontal Method: (x + 3)(x² + 2x + 4)  = x³ + 2x² + 4x + 3x² + 6x + 12Write terms in descending order…  = x³ + 2x² + 3x² + 4x + 6x + 12 Combine like terms = x³ + 5x² + 10x + 12

  9. Vertical Method: x² + 2x + 4 x + 3 x³ + 2x² + 4x 3x² + 6x + 12 x³ + 5x² + 10x + 12

  10. OK, your turn… Please use whiteboard or your notebook: (x+1)(x²+2x+1) (b2 + 6b –7)(3b – 4) (2x2 + 5x –1)(4x – 3) (2y – 3)(3y2 – y + 5) (x2 + 2x + 1)(x + 2)

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