Analyzing Patterns when Multiplying Polynomials Carol A. Marinas, Ph.D.

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Presentation transcript:

Analyzing Patterns when Multiplying Polynomials Carol A. Marinas, Ph.D.

Using the Distributive Property When multiplying terms together, use the distributive property and then simplify. Example: (x + 4) ( x + 3) = x (x + 3) + 4 (x + 3) =(x 2 + 3x) + (4x + 12) = x 2 + 7x + 12

Pattern Recognition: Sum and Difference of the same 2 terms Example: (x + 2) (x - 2) = x (x - 2) + 2 (x- 2)= (x 2 - 2x) + (2x - 4) = x Pattern: (a - b) ( a + b) OR (a + b) ( a - b) = a 2 - b 2

Pattern Recognition: Square of a Binomial Example ( x + 3 ) 2 = (x + 3) (x + 3) = x(x + 3) + 3(x + 3) = (x 2 + 3x) + (3x + 9)= x 2 + 6x + 9 Pattern (x + a) 2 = x ax + a 2 Note : ( x - 3) 2 = x 2 - 6x + 9 Because a = -3 so x 2 + 2(-3)x + 9

Pattern Recognition: Form (x + a) (x + b) Example: (x + 2) ( x + 5) = x(x + 5) + 2 (x+ 5) = (x 2 + 5x) + (2x + 10) = x 2 + 7x + 10 Pattern: (x + a) ( x + b) = x 2 + (a+b)x + ab Note: (x - 3) (x + 5) = x 2 + 2x - 15 because a = -3 and b = 5. So a+b = 2 and ab = -15.

Pattern Recognition Form (x + a)(x 2 - ax + a 2 ) Example: (x +3) (x 2 -3x + 9)= x (x 2 -3x + 9) + 3 (x 2 -3x + 9)= x 3 - 3x 2 + 9x + 3x 2 - 9x + 27= x Pattern: (x + a) (x 2 -ax + a 2 ) = x 3 + a 3 OR (x - a) (x 2 + ax + a 2 ) = x 3 - a 3

Hope this helps... To Make Your Multiplying Easier