Quadratic Equations?

I don't get how we're supposed to FOIL this quadratic equation...

I know how to FOIL, of course, but I don't get how they got the -10x here. Can anyone help me out? These are the steps it showed:

f(x) = 2(x – 5)2

f(x) = 2(x^2 – 10x 25)

f(x) = 2x^2 – 20x 50

Update:

Sorry, the equation got messed up a bit. It should read like this:

f(x) = 2(x – 5)2

f(x) = 2(x^2 – 10x + 25)

f(x) = 2x^2 – 20x + 50)

6 Answers

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  • 1 decade ago
    Favorite Answer

    When you expand (x-5)^2, the first step should look like this:

    x*x+x*-5+-5*x+-5*-5

    Then:

    x^2-5x-5x+25

    x^2-10x+25

    It's -10x because there are two -5x's that add together.

    A good rule to remember is that:

    (a-b)^2=a^2-2ab+b^2

    In this case, "-2ab" is -2*x*5, or -10x

    The fully expanded quadratic is:

    2(x^2-10x+25)

    2x^2-20x+50

  • 1 decade ago

    You can rewrite the (x - 5)² as (x - 5)(x - 5)

    That should help you see where the -10x comes from:

    f(x) = 2(x - 5)²

    f(x) = 2(x - 5)(x - 5) --> Now you can FOIL the (x - 5)(x - 5)

    f(x) = 2(x² - 5x - 5x + 25) --> Combine the like terms: -5x - 5x

    f(x) = 2(x² - 10x + 25) --> Then distribute the 2

    f(x) = 2x² - 20x + 50

  • 1 decade ago

    i think you meant 2(x-5)^2

    so cuz it is to the power of 2 it can be expanded into

    2(x-5)(x-5) and then you foil it

    then you get 2(x^2-10x+25)

    if you time the whole equation by 2

    you get 2x^2-20x+50

    hope this helpz!

  • Anonymous
    1 decade ago

    f(x)=2(x-5)^2

    f(x)=2(x - 5)(x - 5)

    FOIL = First, Outside, Inside, Last

    First = x * x = x^2

    Outside = x * -5 = -5x

    Inside = -5 * x = -5x

    Last = -5 * -5 = 25

    x^2 - 5x - 5x + 25 = x^2 - 10x + 25

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  • 1 decade ago

    The equation should readf(x) = 2(x-5)^2

    (x-5)^2 is (x-5)*(x-5)

    F x*x = x^2

    O x*-5 = -5x

    I x*-5 =-5x

    L -5*-5 =25

    x^2 -5x -5x + 25

    x^2 -10x +25

    then 2(x^2 -10x +25) = 2x^2 -20x +50

    Hope this helps

  • 1 decade ago

    /

    1)2x^2-20x+50

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