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A=1+5+52+53+...+550
=> 5A=(5+52+53+...+550)+551
=> 5A-A=551-1
4A=551-1 => \(A=\frac{5^{51}-1}{4}\)
Bài 2:
\(B=\dfrac{2^{15}\cdot5^8-2^5\cdot2^9\cdot5^9}{2^{16}\cdot5^7+2^{16}\cdot5^8}=\dfrac{2^{14}\cdot5^8\left(2-5\right)}{2^{16}\cdot5^7\left(1+5\right)}=\dfrac{5}{4}\cdot\dfrac{-3}{6}=\dfrac{5}{4}\cdot\dfrac{-1}{2}=-\dfrac{5}{8}\)
1. \(\frac{125^{10}.8^{30}}{5^{29}.2^{60}}\) = \(\frac{5^{30}.2^{90}}{5^{29}.2^{60}}\) = ............
Kl ............
Ta có: a)(x - 5).(2x +3) - (2x -1).(x +7) - (x -1).(x+2)
= 2x2 + 3x - 10x - 15 - 2x2 - 14x + x + 7 - x2 - 2x + x + 2
= -x2 - 21x - 6
a: \(=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)\)
\(=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\)
\(=x^3-16x^2+25x\)
b: \(=\left(a-b+c-b+c\right)\left(a-b+c+b-c\right)+2ab-2ac\)
\(=\left(a-2b+2c\right)\cdot a+2ab-2ac\)
\(=a^2-2ab+2ac+2ab-2ac=a^2\)
c: \(\left(3x+1\right)^2-2\left(3x+1\right)\left(3x+5\right)+\left(3x+5\right)^2\)
\(=\left(3x+1-3x-5\right)^2=\left(-4\right)^2=16\)