**Use these patterns** to factor polynomials 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)

a)x+8 $\displaystyle \textcolor{red}{(\sqrt[3]{x})^2 + 2^3}$

b)8x^3+27 $\displaystyle \textcolor{red}{(2x)^3 + 3^3}$

c)64-y^3 $\displaystyle \textcolor{red}{4^3 - y^3}$

d)2u^3 + 16V^3 $\displaystyle \textcolor{red}{2[u^3 + (2v)^3]}$

e)d^5 + f^3 $\displaystyle \textcolor{red}{(d^{\frac{5}{3}})^3 + f^3}$

f) w^6 -1 $\displaystyle \textcolor{red}{(w^2)^3 - 1^3}$

2. if the sum of two numbers is 6 and the sum of their cubes is 18, what's the sum of their squares?

$\displaystyle \textcolor{red}{x+y = 6}$

$\displaystyle \textcolor{red}{x^3+y^3 = 18}$

also, note that $\displaystyle \textcolor{red}{(x+y)^2 = 36}$

3. use synthetic division to find (x^2 + 4) / (s - 2i)

Code:

2i] 1 ..... 0 ...... 4
----------------------