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Math Help - Polynomials/Factor

  1. #1
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    Polynomials/Factor

    I've gone through my notes and I can't find any to help me solve the following, could anyone help me please?

    1. Multiply:
    (n+6)3

    Do you do n3+216?

    2. Factor:
    x3+125

    3. Factor:
    16a4-1
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  2. #2
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    Re: Polynomials/Factor

    Quote Originally Posted by Kibbygirl View Post
    I've gone through my notes and I can't find any to help me solve the following, could anyone help me please?

    1. Multiply:
    (n+6)3

    Do you do n3+216?

    2. Factor:
    x3+125

    3. Factor:
    16a4-1
    1. Absolutely not. Either write it out in full as \displaystyle \begin{align*} (n + 6)(n + 6)(n + 6) \end{align*} and expand, or apply \displaystyle \begin{align*} (a + b)^3 = a^3 + 3a^2b + 3a\,b^2 + b^3 \end{align*}.

    2. Apply the sum of two cubes rule.

    3. Write it as \displaystyle \begin{align*} \left(4a^2\right)^2 - 1^2 \end{align*} and apply the Difference of Two Squares rule.
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  3. #3
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    Re: Polynomials/Factor

    (a+b)^3=a^3+3a^2b+3ab^2+b^3

    a^3+b^3=(a+b)(a^2-ab+b^2)

    a^4-b^4=(a-b)(a+b)(a^2+b^2)
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