Simplify the Following Product
\[ (x^3 – 3x^2 – x)(x^2 – 3x + 1) \]
Solution:
\[ = x(x^2 – 3x – 1)(x^2 – 3x + 1) \]
\[ = x\left[(x^2 – 3x)^2 – 1^2\right] \]
Using identity:
\[ (a-b)(a+b)=a^2-b^2 \]
\[ = x\left(x^4 + 9x^2 – 6x^3 – 1\right) \]
\[ = x^5 – 6x^4 + 9x^3 – x \]