Simplify the Following Product
\[ (2x^4 – 4x^2 + 1)(2x^4 – 4x^2 – 1) \]
Solution:
\[ = \left[(2x^4 – 4x^2)+1\right] \left[(2x^4 – 4x^2)-1\right] \]
Using identity:
\[ (a+b)(a-b)=a^2-b^2 \]
\[ = (2x^4 – 4x^2)^2 – 1^2 \]
\[ = (2x^4)^2 + (4x^2)^2 – 2(2x^4)(4x^2) – 1 \]
\[ = 4x^8 + 16x^4 – 16x^6 – 1 \]
\[ = 4x^8 – 16x^6 + 16x^4 – 1 \]