5.3 Multiplying Polynomials

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

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?

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

Activity I need 7 volunteers.

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

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

(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.

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

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

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.

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.

a - b a - b a2 – b2 = (a – b)(a + b)

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

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.

Class Assignment 5.3 pg. 217 # 2 – 36 even