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Math Help - Distributive Law of Multiplication Using Variables

  1. #1
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    Distributive Law of Multiplication Using Variables

    I'm having some trouble with this concept. Expression:

    3x(4x + 5)

    and another one

    -2x(3x - 12)
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  2. #2
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    Recall a(b+c) = a\times b +a\times c

    Therefore

     2x(7x+4) = 2x\times 7x+2x\times 4 = 14x^2+8x

    and

     -12x(6x-3) = -12x\times 6x-12x\times -3 = -72x^2+36x

    Use these examples to do yours.
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  3. #3
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    3x(4x + 5)
    3x(4x) + 3x(5)
    12x^2 + 15x

    -2x(3x - 12)
    -2x(3x) -2x(-12)
    -6x^2 + 24x
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  4. #4
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    Thanks. I have another question, what's 14x^2 + x^2?

    Is that 15x^2?
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  5. #5
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    And 2x(x + 3) = 3x + 3? Or 2x^2 + 3?
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  6. #6
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    Quote Originally Posted by ahhlecks View Post
    Thanks. I have another question, what's 14x^2 + x^2?

    Is that 15x^2?
    Yep
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  7. #7
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    Quote Originally Posted by ahhlecks View Post
    And 2x(x + 3) = 3x + 3? Or 2x^2 + 3?
    Neither, 2x(x + 3) = 2x^2 + 6x
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  8. #8
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    Thank you.

    This one's got me stumped.

    4x^2(5x + 6) + 2x(x^2 + 10x - 12)
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  9. #9
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    I got

    20x^3 + 24x^2 + 4x^3 + 20x^2 - 24x

    = 24x^3 + 44x^2 - 24x
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