Find the Product:
\[ (x^3 + 1)(x^6 – x^3 + 1) \]
Solution:
Using identity:
\[ (a+b)(a^2-ab+b^2)=a^3+b^3 \]
Here, \[ a=x^3,\qquad b=1 \]
\[ (x^3 + 1)(x^6 – x^3 + 1) \]
\[ = (x^3 + 1)\left[(x^3)^2 – (x^3)(1) + 1^2\right] \]
\[ = (x^3)^3 + 1^3 \]
\[ = x^9 + 1 \]