Analyzing Patterns when Multiplying Polynomials - PowerPoint PPT Presentation

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Analyzing Patterns when Multiplying Polynomials

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  1. Analyzing Patterns whenMultiplying Polynomials Carol A. Marinas, Ph.D.

  2. 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) =(x2 + 3x) + (4x + 12) = x2 + 7x + 12

  3. Example: (x + 2) (x - 2) = x (x - 2) + 2 (x- 2)= (x2-2x) + (2x - 4) = x2 - 4 Pattern: (a - b) ( a + b) OR (a + b) ( a - b) = a2 - b2 Pattern Recognition:Sum and Difference of the same 2 terms

  4. Example ( x + 3 ) 2 = (x + 3) (x + 3) = x(x + 3) + 3(x + 3) = (x2 + 3x) + (3x + 9)= x2 + 6x + 9 Pattern (x + a) 2 = x2 + 2 ax + a2 Note : ( x - 3)2 = x2 - 6x + 9 Because a = -3 so x2 + 2(-3)x + 9 Pattern Recognition:Square of a Binomial

  5. Example: (x + 2) ( x + 5) = x(x + 5) + 2 (x+ 5) = (x2 + 5x) + (2x + 10) = x2 + 7x + 10 Pattern: (x + a) ( x + b) = x2 + (a+b)x + ab Note: (x - 3) (x + 5) = x2 + 2x - 15 because a = -3 and b = 5. So a+b = 2 and ab = -15. Pattern Recognition:Form (x + a) (x + b)

  6. Example: (x +3) (x2 -3x + 9)= x (x2 -3x + 9) + 3 (x2 -3x + 9)= x3- 3x2 + 9x + 3x2 - 9x + 27= x3 + 27 Pattern: (x + a) (x2 -ax + a2) = x3 + a3 OR (x - a) (x2 + ax + a2) = x3 - a3 Pattern RecognitionForm (x + a)(x2 - ax + a2)

  7. Hope this helps ... To Make Your Multiplying Easier