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Math Help - How do I simplify this since it's too long to use foil?

  1. #1
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    How do I simplify this since it's too long to use foil?

    The problem is: (3x^2+5x+4)(-5x^2-x+3)


    Would I distribute 3x^2 to -5x^2, then to -x, and then to 3, and then do the same with 5x and 4?


    I'm just kinda confused because there are "+" signs within the parenthesis, but not in between them. That's throwing me off for some reason. I can't remember how you do all the different types of these problems (like ones that are multiplication, versus adding, etc...)
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  2. #2
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    Hello, deathtolife04!

    The problem is: . (3x^2+5x+4)(-5x^2-x+3)

    Would I distribute 3x^2 to -5x^2, then to -x, and then to 3
    and then do the same with 5x and 4? . . . . Yes!
    In general, we multiply each term in the first polynomial by each term in the second.
    . . Don't let the signs confuse you . . . just "bring them along".


    We wil have: . (3x^2)(-5x^2)\;\;\;(3x^2)(-x)\;\;\;(3x^2)(3)\;\;\;(5x)(-5x^2)\;\;\;(5x)(-x)\;\;\;(5x)(3) . (4)(-5x^2)\;\;\;(4)(-x)\;\;\;(4)(3)


    Then combine these products: . -5x^4 - 3x^3 + 9x^2 - 25x^3 - 5x^2  + 15x - 20x^2 -4x + 12

    . . = \;-15x^4 - 28x^3 - 16x^2 + 11x + 12

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