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Math Help - Questions regarding my next phase in self taught algebra

  1. #1
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    Questions regarding my next phase in self taught algebra

    Hello everyone, I have almost completed the self teaching guide through Algebra I. The last chapters end with quadratic polynomial expressions, equations, and applications e.g. in the form  ax^2+bx+c

    While I was surfing through some posts today I stumbled across this expression. Im not sure what to call (8a^3+1) because it is not a quadratic expression yet it is factored in a seemingly similar manner.

    <br />
(8a^3+1)=(1+2a)(1-2a+4a^2)


    Would some one please tell me what this type of expression is and what the rules for factoring it are?

    Also when might I expect to see expressions beyond quadratic polynomials? Algebra II?


    Thank you
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  2. #2
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    Quote Originally Posted by allyourbass2212 View Post
    Hello everyone, I have almost completed the self teaching guide through Algebra I. The last chapters end with quadratic polynomial expressions, equations, and applications e.g. in the form  ax^2+bx+c

    While I was surfing through some posts today I stumbled across this expression. Im not sure what to call (8a^3+1) because it is not a quadratic expression yet it is factored in a seemingly similar manner.

    <br />
(8a^3+1)=(1+2a)(1-2a+4a^2)


    Would some one please tell me what this type of expression is and what the rules for factoring it are?

    Also when might I expect to see expressions beyond quadratic polynomials? Algebra II?


    Thank you
    The formula they're using to factor this is the sum/difference of two cubes - a special case when factoring cubics:

    a^3 \pm b^3 = (a+b)(a^2 \mp ab + b^2)

    In your case a = (2a) and b=1
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  3. #3
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    This type of question trips people up because (8a^3+1) doesnt seem to belong to the factoring equation x^3+y^3=(x+y)(x^2-xy+y^2) when it actually does.

    Note that (8a^3+1)=((2a)^3+1^3)

    Now just apply that to x^3+y^3=(x+y)(x^2-xy+y^2).
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