6.3 adding, subtracting, and mulitplying polynomials

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6.3 adding, subtracting, and mulitplying polynomials

  1. 1.  Add the coefficients of like terms. Can be done vertically or horizontally. Example: Add and Vertical Method: Horizontal Method:
  2. 2.  Add the polynomials:
  3. 3.  Subtract the coefficients of like terms. Example: Subtract Vertical Method: Horizontal Method:
  4. 4.  Subtract the polynomials.
  5. 5.  Each term of the first must be multiplied by each term of the second. Similar to multiplying large numbers by hand. Example: 385 -x2 +2x +4 x 24 x x-3
  6. 6.  Multiply the first polynomial by each term of the second. Then, distribute and combine like terms. Example:
  7. 7.  Multiply
  8. 8.  Multiply the polynomials:
  9. 9.  FOIL two of the binomials first Then, multiply the two resulting polynomials. Example:
  10. 10.  Multiply
  11. 11.  Sum and Difference:(a + b)(a – b) = a2 – b2Example: (4n - 5)(4n + 5) Square of a Binomial:(a + b) 2 = a2 + 2ab + b2 (a - b) 2 = a2 - 2ab + b2Example: (9y – x2)2
  12. 12. (a + b) 3 = a3 + 3a2b + 3ab2 + b3 (a - b) 3 = a3 - 3a2b + 3ab2 - b3 Examples: (x + 1)3 (xy – 2)3
  13. 13.  Multiply: (5x + 2)2 (3x - 2)(3x + 2) (2m – 3)3

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