Find the Product:
\[ (x^2 – 1)(x^4 + x^2 + 1) \]
Solution:
Using identity:
\[ (a-b)(a^2+ab+b^2)=a^3-b^3 \]
Here, \[ a=x^2,\qquad b=1 \]
\[ (x^2 – 1)(x^4 + x^2 + 1) \]
\[ = (x^2 – 1)\left[(x^2)^2 + (x^2)(1) + 1^2\right] \]
\[ = (x^2)^3 – 1^3 \]
\[ = x^6 – 1 \]