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1951 AMC 12 Question 40

AMC12 · 1951 AMC 12

Question 40

The expression $$
\begin{aligned} &\left(\frac{(x+1)^2(x^2-x+1)^2}{(x^3+1)^2}\right)^2\\ &\quad{}\cdot \left(\frac{(x-1)^2(x^2+x+1)^2}{(x^3-1)^2}\right)^2 \end{aligned}
$$ equals:
  1. $(x+1)^4$
  2. $(x^3+1)^4$
  3. $1$
  4. $\big[(x^3+1)(x^3-1)\big]^2$
  5. $\big[(x^3-1)^2\big]^2$