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