Simplify the Following
\[ (x+3)^3+(x-3)^3 \]
Solution:
Using identity:
\[ a^3+b^3=(a+b)(a^2-ab+b^2) \]
\[ = [(x+3)+(x-3)] \left[(x+3)^2-(x+3)(x-3)+(x-3)^2\right] \]
\[ = (2x)\left[(x^2+6x+9)-(x^2-9)+(x^2-6x+9)\right] \]
\[ = (2x)(x^2+27) \]
\[ = 2x^3+54x \]