Question

Rút gọn biểu thức (3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)

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Answer 1

Ta có: \(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(=\dfrac{\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2}\)

\(=\dfrac{\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2}\)

\(=\dfrac{\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2}\)

\(=\dfrac{\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)}{2}\)

\(=\dfrac{\left(3^{16}-1\right)\left(3^{16}+1\right)}{2}\)

\(=\dfrac{3^{32}-1}{2}\)

Answer 2

Rút gọn: (3 + 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)
A=(3 + 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(316 + 1)(3³² + 1)

A=2(3 + 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)

A=(3-1)(3 + 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)
A=(3²-1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)
A=(3⁴-1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)
A=(3⁸-1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1)
A=(3¹⁶-1)(3¹⁶ + 1)(3³² + 1)
A=(3³² - 1)(3³² + 1)
A=3⁶⁴-1
=>A=(3⁶⁴-1) /2