Question

C1: Rút gọn

a, (\(\left(3^2+1\right)\left(3^4+1\right)....\left(3^{1024}+1\right)\)

b, \(100^2-99^2+98^2-97^2+...+50^2-49^2\)

c, ( x -1)^2 + (x-2)x(x+2) -(x+3)^3

Giúp mị vs T^T

Answer 1

a: \(=\dfrac{\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\cdot...\cdot\left(3^{1024}+1\right)}{8}\)

\(=\dfrac{\left(3^4-1\right)\left(3^4+1\right)\cdot...\cdot\left(3^{1024}+1\right)}{8}\)

\(=\dfrac{3^{2048}-1}{8}\)

b: \(=100+99+98+97+...+50+49\)

Số số hạng là (100-49):1+1=100-48=52 số

Tổng là (100+49)*52/2=149*26=3874

c: \(=x^2-2x+1+x^2-4-x^3-9x^2-27x-27\)

\(=-x^3-7x^2-29x-30\)