\(A=3\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)...\left(x^{64}+1\right)\)
\(\Leftrightarrow A=\frac{3\left(x^2-1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\left(x^{16}+1\right)\left(x^{32}+1\right)\left(x^{64}+1\right)}{x^2-1}\)
\(\Leftrightarrow A=\frac{3\left(x^4-1\right)\left(x^4+1\right)\left(x^8+1\right)\left(x^{16}+1\right)\left(x^{32}+1\right)\left(x^{64}+1\right)}{x^2-1}\)
\(\Leftrightarrow A=\frac{3\left(x^8-1\right)\left(x^8+1\right)\left(x^{16}+1\right)\left(x^{32}+1\right)\left(x^{64}+1\right)}{x^2-1}\)
\(\Leftrightarrow A=\frac{3\left(x^{16}-1\right)\left(x^{16}+1\right)\left(x^{32}+1\right)\left(x^{64}+1\right)}{x^2-1}\)
\(\Leftrightarrow A=\frac{3\left(x^{32}-1\right)\left(x^{32}+1\right)\left(x^{64}+1\right)}{x^2-1}\)
\(\Leftrightarrow A=\frac{3\left(x^{64}-1\right)\left(x^{64}+1\right)}{x^2-1}\)
\(\Leftrightarrow A=\frac{3\left(x^{128}-1\right)}{x^2-1}\)