Algebra - Polynomials Multiplication

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Author:
randycapped
ID:
267638
Filename:
Algebra - Polynomials Multiplication
Updated:
2014-03-24 01:24:19
Tags:
Polynomials
Folders:
Algebra
Description:
Multiplying Polynomials
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  1. Multiplying monomials.



    =
  2. Multiplying monomials.




    =  
  3. Multiplying monomials.




    =
  4. Multiplying a Monomial by a Polynomial.



  5. Multiplying a Monomial by a Polynomial.



  6. Multiplying Binomials.

    *Each term in the first polynomial must be multiplied by each term in the second.

    +



  7. Multiplying Binomials.

    *Each term in the first polynomial must be multiplied by each term in the second.





  8. Multiplying a binomial by a trinomial.

    *Each term in the first polynomial must be multiplied by each term in the second.

    x(5x2)+x(-2x)+x(-6)+4(5x2)+4(-2x)+4(-6)

    5x3-2x2-6x+20x2-8x-24

  9. Formula for "Special Case Products"

    The product of congugates results in a ______ of ________.

    The square of a binomial results in a _______ _______ trinomial.
    • difference
    • squares
    • perfect
    • square

  10. Special Case Formula #1:



    a2-ab + ab -b2



    (difference of squares)
  11. Special Case Formula #2:

    • (a+b)(a+b)
    • a2+ab+ab+b2

    (perfect square trinomial)
  12. The product of conjugates results in a ______ of _______.
    • difference
    • squares
  13. The square of a binomial results in a _______ _______ trinomial.
    • perfect
    • square
  14. Find a polynomial that represents the volume of the cube:




    V= (x+4)(x+4)(x+4)

    Step 1: Multiplying from left to right, you notice that you're squaring a binomial. So, you'll get a perfect square trinomial.

    • Step 2: Rewrite the equation:
    •  



    Step 3: Multiply each term in first parentheses by each term in the 2nd.

    x2*x+x2*4+8x*x+8x*4+16*x+16*4

    x3 + 4x2 + 8x2 + 32x + 16x + 64

    Step 4: Combine like terms:

    V =
  15. Multiplying Conjugates.

    Once you recognize the conjugate, you know you will end up with a difference in squares, so you don't have to multiply the "long way".



  16. Multiplying Conjugates.

    Once you recognize the conjugate, you know you will end up with a difference in squares, so you don't have to multiply the "long way".



  17. Squaring Binomials.

    We know that the result will be a perfect square trinomial. So, you don't have to multiply (a+b)(a+b) the long way.

     (2x)2 +2(2x)(5) + (5)2

    • SAME AS:

  18. Squaring Binomials.

    We know that the result will be a perfect square trinomial. So, you don't have to multiply (a+b)(a-b) the long way. Just remember to put the negative sign in front of the middle term.

    (3y2)2 - 2(3y2)(7w) + (7w)2

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