Multiplying Binomials and Special Cases

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Multiplying Binomials

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Multiplying Binomials and Special Cases Pearson 11.3 and 11.4

(2x – 6)(3x + 2) Distributive Method Distribute the first binomial 2x(3x + 2) – 6(3x + 2) Multiply 6x2 + 4x – 18x – 12 Simplify 6x2 – 14x – 12

(3x + 4)(5x – 4) Using a Table Set up table Multiply and fill in blanks Simplify 15x2 + 8x – 16 5x –4 3x 15x2 -12x 4 20x -16

(5x + 2)(6x – 4) FOIL Method – 8 F – First Terms 30x2 O – Outer Terms I – Inner Terms 12x L – Last Terms – 8 Simplify 30x2 – 8x – 8

Multiplying a Binomial and Trinomial (2x2 – 4x + 1)(5x + 7) Set up Table 2x2 -4x 1 5x 10x3 -20x2 7 14x2 -28x Simplify 10x3 – 6x2 – 23x + 7

Be Very Careful!!!! (3x + 5)2 = (3x + 5)(3x +5) It does not equal Square of a Binomial (3x + 5)2 Be Very Careful!!!! (3x + 5)2 = (3x + 5)(3x +5) It does not equal (3x)2 + (5)2 (a + b)2 = a2 + 2ab + b2 a = 3x b = 5 Substitute (3x)2 + 2(3x)(5) + (5)2 Solve and Simplify 9x2 + 30x + 25

(4x – 6)2 Square of a Binomial (a – b)2 = a2 – 2ab + b2 a = 4x b = 6 Substitute (4x)2 – 2(4x)(6) + (6)2 Solve and Simplify 16x2 – 48x + 36

Product of a Sum and Difference (5x – 3)(5x + 3) (a – b)(a + b) = a2 – b2 a = 5x b = 3 Substitute (5x)2 – (3)2 Solve and Simplify 25x2 – 9