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Math 9 Lesson #32 – Multiplying Polynomials Mrs. Goodman

Math 9 Lesson #32 – Multiplying Polynomials Mrs. Goodman. Multiplying Binomials. First, let’s look at how to multiply two binomials!. Multiplying Binomials. (3x + 4)(2x – 1) Think of the distributive property…. Multiplying Binomials. (3x + 4)(2x – 1)

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Math 9 Lesson #32 – Multiplying Polynomials Mrs. Goodman

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  1. Math 9 Lesson #32 – Multiplying Polynomials Mrs. Goodman

  2. Multiplying Binomials • First, let’s look at how to multiply two binomials!

  3. Multiplying Binomials • (3x + 4)(2x – 1) • Think of the distributive property…

  4. Multiplying Binomials • (3x + 4)(2x – 1) • We are going to distribute using the FOIL method

  5. Multiplying Binomials • (3x + 4)(2x – 1) • First • OuterInnerLast

  6. Multiplying Binomials • (3x + 4)(2x – 1) • (3x)(2x) + (3x)(-1) + (4)(2x) + (4)(-1) • 6x2 – 3x + 8x – 4 • 6x2 + 5x - 4

  7. Multiplying Binomials • (x - 6)(3x + 3) • (x)(3x) + (x)(3) + (-6)(3x) + • (-6)(3) • 3x2 + 3x - 18x – 18 • 3x2 - 15x - 18

  8. Multiplying Polynomials • (x + 1)(3x2 + 4x + 2) • = (3x2)(x + 1) + (4x)(x + 1) + • (2)(x + 1) • = 3x3 + 3x2 + 4x2 + 4x + 2x + 2 • = 3x3 + 7x2 + 6x + 2

  9. Multiplying Polynomials • (2x + 2)(x2 + 5x - 6) • = (x2)(2x + 2) + (5x)(2x + 2) + • (-6)(2x + 2) • = 2x3 + 2x2 + 10x2 + 10x + -12x -12 • = 2x3 + 12x2 – 2x - 12

  10. Let’s try some! • (-4x)(2x + 5) • (2y + 4)(4y – 5) • (2x + 6)(-3x2 + 4x – 3)

  11. Special Products • (a + b)(a – b) = a2 – b2

  12. Special Products • Example: • (x + 4)(x – 4) = • x2 - 16

  13. Special Products • (a + b)2 = a2 + 2ab + b

  14. Special Products • Example: • (x + 7)2 • x2 + 14x + 49

  15. Special Products • (a - b)2 = a2 - 2ab + b

  16. Special Products • Example: • (x - 8)2 • x2 – 16x + 64

  17. That’s all for today! • Thanks for working hard! • See you next time!

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