Question

rút gọn biểu thức A=12(5 mũ 2 +1)(5 mũ 4+1)(5 mũ 8 +1)(5 mũ 16+1)-5 mũ 32

Answer 1

\(A=\dfrac{\left(5^2-1\right)\left(5^2+1\right)\cdot...\cdot\left(5^{16}+1\right)}{2}-5^{32}\)

\(=\dfrac{\left(5^4-1\right)\left(5^4+1\right)\cdot...\cdot\left(5^{16}+1\right)}{2}-5^{32}\)

\(=\dfrac{5^{32}-1-2\cdot5^{32}}{2}=\dfrac{-5^{32}-1}{2}\)