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5.3 Multiplying Polynomials

5.3 Multiplying Polynomials. Brett Solberg – AHS – ’11-’12. Warm-up. October 26 2011 #1 P(x) = 2x 2 y 3 + 8z 5 Q(X) = 5z 8 – 4x 2 y 3 Find P(x) + Q(x) Find Q(x) – P(x) #2 Distribute the following x(2x + 4) (x + 4)(2x – 1) Do you have any HW questions?. Today’s Agenda.

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5.3 Multiplying Polynomials

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  1. 5.3 Multiplying Polynomials Brett Solberg – AHS – ’11-’12

  2. Warm-up • October 26 2011 • #1 P(x) = 2x2y3 + 8z5 Q(X) = 5z8 – 4x2y3 • Find P(x) + Q(x) • Find Q(x) – P(x) • #2 Distribute the following • x(2x + 4) • (x + 4)(2x – 1) • Do you have any HW questions?

  3. Today’s Agenda • Multiplying Polynomials • Distribution • Binomials • FOIL • Squaring Binomials • Multiplying Sums and Differences • Reminder: End of Quarter

  4. Activity • I need 7 volunteers.

  5. Distribution • Milk Duds(Bob + Sue) = M.D Bob + M.D Sue • a(b + c) = ab + ac • 2(x + 3) = 2x + 6 • x(3x – 4) = 3x2 – 4x

  6. FOIL The order you multiply terms F - First O - Outside I - Inside L - Last (Reeses + Rolo)(Megan + Jack) Reeses Megan + Reeses Jack + Rolo Megan + Rolo Jack (a + b)(c + d) = ac + ad + bc + bd (x + 3)(2x + 7) = 2x2 + 7x + 6x + 21

  7. (a + b)(c + d + e) = ac + ad + ae + bc + bd + be (x + 2)(x2 -4x + 3) = x3 - 4x2 + 3x + 2x2 – 8x + 6 x3 – 2x2 - 5x + 6 Do the first 3 examples on your worksheet.

  8. Squaring Sums • (a + b)2 • (a+ b)(a +b) • a2 + 2ab + b2 • (2x + 7y)2 • a = 2x b = 7y • (2x)2 + 2*2x*7y + (7y)2 • 4x2 + 28XY + 49y2 • Do example 5 on the worksheet

  9. a a a2 b ab b (a + b)2 a2 + 2ab + b2 b ab a b2 b b

  10. Squaring Sum Activity • Fold graph paper in half. • In the top left corner make a square less that 10 x 10 units. • From the bottom left corner of the square make another square less than 10 x 10 units. • Make a big square containing both these squares and label all the sides.

  11. Squaring Differences • (a - b)2 • (a - b)(a - b) • a2- 2ab + b2 • (4x2 - 16)2 • a = 4x2 b = 16 • (4x2)2 – 2*4x2*16 + 162 • 16x4 – 128x2 + 256 • Do example 4 on the worksheet.

  12. a - b a - b a2 – b2 = (a – b)(a + b)

  13. Multiplying Sum and Difference • (a + b)(a – b) = a2 – b2 • (2x + 4)(2x – 4) • 4x2 - 8x + 8x – 16 • 4x2 – 16 • (3xy2 + 8)(3xy2 – 8) • (3xy2)2 – 82 • 9x2y4 – 64 • Do example 6

  14. Combination • (x + 3)(x – 3)(2x + 1) • Multiplication of Sum and Difference • (x2 – 9)(2x + 1) • FOIL • 2x3 + x2 -18x – 9 • Do example 7 and 8.

  15. Class Assignment • 5.3 pg. 217 # 2 – 36 even

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