Math (Factoring Sums and Difference of Cubes)

Discussion in 'Community Discussion' started by waloshin, Mar 30, 2009.

  1. waloshin macrumors 68040

    waloshin

    Joined:
    Oct 9, 2008
    #1
    Sometimes I am stupid , but anyways:

    27 + (2a -5)^2

    The answer is (2a) (9 -6a + 15 + 4a -20a +25)

    Where does the -20a come from

    (x+6)^3 -y^3

    The answer is (x + 6)(x^2 + 12x + 36 + xy + 6y + y^2)

    Where does the 12x come from

    Thanks
     
  2. Doctor Q Administrator

    Doctor Q

    Staff Member

    Joined:
    Sep 19, 2002
    Location:
    Los Angeles
    #2
    That answer can't be correct since every term has an 'a' in it. For example, if a=0 then we have
    27 + (2a -5)^2
    = 27 + (0-5)^2
    = 27 + (-5)^2
    = 27 + 25
    = 52​
    but
    (2a) (9 - 6a + 15 + 4a -20a +25)
    (2x0) (9 - 6x0 + 15 + 4x0 -20x0 +25)
    0 (9 - 0 + 15 + 0 - 0 +25)
    0​
    They aren't equal, so that answer is wrong. Who told you it was right?

    Let's do the problem correctly instead. When you multiple 2a-5 by 2a-5, you multiply all four combinations of terms. It's the FOIL rule: First, Outside, Inside, Last.:
    27 + (2a -5)^2
    27 + (2a -5) x (2a -5)
    27 + (2a x 2a) + (2a x -5) + (-5 x 2a) + (-5 x -5)​
    Simplifying each term:
    27 + (2a x 2a) + (2a x -5) + (-5 x 2a) + (-5 x -5)
    27 + 4a^2 - 10a - 10a + 25​
    Combining like terms:
    27 + 4a^2 - 10a - 10a + 25
    4a^2 + (-10a -10a) + (27 + 25)
    4a^2 - 20a + 52​
     

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