Polynomials/Factor

**Kibbygirl** · April 27th 2012, 08:35 PM

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

**Prove It** · April 27th 2012, 08:50 PM

Originally Posted by Kibbygirl

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.