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9.7 MULTIPLYING POLYNOMIALS

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1 9.7 MULTIPLYING POLYNOMIALS
You will learn: to multiply two binomials to multiply any two polynomials

2 Review: Multiplying Monomial by Polynomial
To multiply a monomial by a polynomial, you must distribute the monomial to each of the terms of the polynomial. -3x(2x2 + 5x – 1) -6x3 – 15x2 + 3x

3 The next one… 10x3(2x2 – 7x + 8) 20x5 – 70x4 + 80x3

4 What about this problem?
3a2b(5a2 + 3ab2 + 5b) 15a4b +9a3b3 + 15a2b2

5 Fractions too? -5x3 +2x2y

6 Ex. 1) Multiplying a Binomial by a Polynomial
(3x – 4)(2x2 + 3x – 8) 3x – 4 Distribute the first term Now distribute the second term – 24x – 8x2 – 12x +32 6x3 +9x2 Now combine like terms 6x3 +x2 – 36x +32

7 Ex. 2) You can also use the table method
(5x2 + 6x)(3x3 + 2x – 9) 5x2 + 6x 3x3 + 2x – 9 15x5 10x3 -45x2 18x4 12x2 -54x 15x5 +18x4 +10x3 – 33x2 – 54x

8 (x + 2)(3x – 8) (5x – 1)(-2x2 + 5x – 9) 3x2 – 2x – 16
Try It! (x + 2)(3x – 8) (5x – 1)(-2x2 + 5x – 9) (3x + 2)(9x2 –12x + 4) 3x2 – 2x – 16 -10x3 + 27x2 – 50x + 9 27x3 – 18x2 – 12x + 8

9 Complete homework Page 539 (14-33)
Special Products tomorrow

10 Therefore: (x + 3)2 (x + 3) (x + 3) REMEMBER: x2 = x·x x2 +3x +3x +9 =
SPECIAL PRODUCTS REMEMBER: x2 = x·x Therefore: (x + 3)2 (x + 3) (x + 3) x2 +3x +3x +9 = x2 +6x +9

11 x2 – 8x + 16 9x2 + 12x + 4 4x2 + 20xy + 25y2 (x – 4)2 (3x + 2)2
Try it! (x – 4)2 (3x + 2)2 (2x + 5y)2 x2 – 8x + 16 9x2 + 12x + 4 4x2 + 20xy + 25y2

12 SPECIAL PRODUCTS (x + 3) (x - 3) x2 - 3x +3x - 9 = x2 +0x - 9 x2 - 9

13 x2 –16 9x2 - 4 4x2 - 25y2 (x – 4)(x + 4) (3x + 2)(3x – 2)
Try it! (x – 4)(x + 4) (3x + 2)(3x – 2) (2x + 5y)(2x – 5y) x2 –16 9x2 - 4 4x2 - 25y2


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