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 n^{3}+216?

2. Factor:

x^{3}+125

3. Factor:

16a^{4}-1

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- Apr 27th 2012, 08:35 PMKibbygirlPolynomials/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 n^{3}+216?

2. Factor:

x^{3}+125

3. Factor:

16a^{4}-1 - Apr 27th 2012, 08:50 PMProve ItRe: Polynomials/Factor
1. Absolutely not. Either write it out in full as $\displaystyle \displaystyle \begin{align*} (n + 6)(n + 6)(n + 6) \end{align*}$ and expand, or apply $\displaystyle \displaystyle \begin{align*} (a + b)^3 = a^3 + 3a^2b + 3a\,b^2 + b^3 \end{align*}$.

2. Apply the sum of two cubes rule.

3. Write it as $\displaystyle \displaystyle \begin{align*} \left(4a^2\right)^2 - 1^2 \end{align*}$ and apply the Difference of Two Squares rule. - Apr 27th 2012, 08:51 PMprincepsRe: Polynomials/Factor
$\displaystyle (a+b)^3=a^3+3a^2b+3ab^2+b^3$

$\displaystyle a^3+b^3=(a+b)(a^2-ab+b^2)$

$\displaystyle a^4-b^4=(a-b)(a+b)(a^2+b^2)$