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Thread: Polynomials of 9th Grade

  1. #1
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    Polynomials of 9th Grade

    Use these patterns to factor polynimials that are sums and differences of cubes:
    a^3 + b^3 = (a+b)(a^2-ab+b^2)
    a^3 - b^3 = (a-b)(a^2-ab+b^2)

    1. x^3 + 8
    2. 8x^3 + 27
    3. 64 - y^3
    4. 2u^3 +16v^3
    5. d^6 + f^3
    6. w^6 - 1



    Please, show work!!!
    Thank You so so much!!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by tecktonikk View Post
    Use these patterns to factor polynimials that are sums and differences of cubes:
    a^3 + b^3 = (a+b)(a^2-ab+b^2) --- (1)
    a^3 - b^3 = (a-b)(a^2-ab+b^2) --- (2)

    1. x^3 + 8
    Note that x^3+8=x^3+(2)^3. Now use (1) to factor..

    2. 8x^3 + 27
    Note that 8x^3+27=(2x)^3+(3)^3. Now use (1) to factor..

    3. 64 - y^3
    Note that 64-y^3=(4)^3-y^3. Now use (2) to factor..

    4. 2u^3 +16v^3
    Note that 2u^3+16v^3=(\sqrt[3]{2}u)^3+(2\sqrt[3]{2}v)^3. Now use (1) to factor..

    5. d^6 + f^3
    Note that d^6+f^3=(d^2)^3+f^3. Now use (1) to factor..

    6. w^6 - 1
    Note that w^6-1=(w^2)^3-1^3. Now use (2) to factor..

    Please, show work!!!
    Thank You so so much!!
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  3. #3
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    Hi tecktonikk

    You have been given the formula. All you have to do is just manipulate the questions so they satisfy the formula given.

    Example :
    x^3 + 8 = x^3 + 2^3 , so a = x and b = 2

    I'm sure you can do the rest ^^

    EDIT : Nice quote at the end, Chris
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