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    andypanda's Avatar
    andypanda Posts: 1, Reputation: 1
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    #1

    Nov 29, 2006, 04:20 PM
    Functions
    I have a few questions concerning functions...
    1) X^3+64
    2) 54p^3-16q^3
    3) 2x^2-5x=3
    4) 2x^2-8x=0
    :confused: :confused:
    worthbeads's Avatar
    worthbeads Posts: 538, Reputation: 45
    Senior Member
    		  
    #2

    Nov 29, 2006, 04:43 PM
    What exactly are you having trouble with?
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
    		  
    #3

    Nov 30, 2006, 07:59 AM
    Quote Originally Posted by andypanda
    I have a few questions concerning functions...
    1) X^3+64
    2) 54p^3-16q^3
    3) 2x^2-5x=3
    4) 2x^2-8x=0
    :confused: :confused:
    It appears you want to factor.

    The first one is the sum of 2 cubes... Easy.

    3 and 4 are completing the square.

    The 2nd one is the difference of 2 cubes, but a little trickier. I'll do it and you try the others.

    54p^3-16q^3

    Factor out 2:

    2(27p^3-8q^3)

    Make into a difference of cibes inside the parentheses:

    2((3p)^3-(2q)^3)

    Now, let x=3p and y=2q:

    2(x^3-y^3)

    Difference of cubes formula:

    2(x-y)(x^2+xy+y^2)

    Resub:

    2(3p-2q)((3p)^2+(3p)(2q)+(2q)^2)

    2(3p-2q)(9p^2+6pq+4q^2)

    Does that help?
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