5.3C- Special Patterns for Multiplying Binomials SUM AND DIFFERENCE (a+b)(a-b) = a² - b² (x +2)(x – 2) = x² -4 “O & I” cancel out of FOIL SQUARE OF A BINOMIAL.

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5.3C- Special Patterns for Multiplying Binomials SUM AND DIFFERENCE (a+b)(a-b) = a² - b² (x +2)(x – 2) = x² -4 “O & I” cancel out of FOIL SQUARE OF A BINOMIAL (a+b)² = a² + 2ab + b² (2x + 3)² = (2x)² + 2(2x)(3) + (3)² = 4x² + 12x + 9 (a – b)² = a² - 2ab + b² (x – 5)² = (x)² - 2(x)(5) + (5)² = x² -10x + 25

More Special Patterns CUBE OF BINOMIAL (a + b)³ = a³ + 3a²b + 3ab² + b³ (x + 2)³ = (x)³ + 3(x)²(2) + 3(x)(2)² + 2³ = x³+6x² + 12x + 8 (a – b)³ = a³ - 3a²b + 3ab² - b³ (2x – 3)³ = (2x)³ - 3(2x)²(3) + 3(2x)(3)² - (3)³ = 8x³ - 36x²+ 54x – 27

Examples: Multiply using patterns 1. (x-3)(x+3) 2. (2x + 7)(2x – 7)

More examples: 3. (x +5)² 4. (2x – 5)²

More examples 5. (3x + 2)³ 6. (x – 4)³