\(Bài.1:\\ a,104^2-16=104^2-4^2=\left(104+4\right)\left(104-4\right)=108.100=10800\\ b,9^8.2^8-\left(18^4-1\right)\left(18^4+1\right)\\ =\left(9.2\right)^8-\left(18^8-1\right)=18^8-18^8+1=1\\ c,999^3+3.999^2+3.999+1\\ =999^3+3.999^2.1+3.999.1^2+1^3=\left(999+1\right)^3=1000^3=1000000000\\ d,42^3-6.42^2+12.42-8\\ =42^3-3.42^2.2+3.42.2^2-2^3\\ =\left(42-2\right)^3=40^3=64000\)
Bài 1
a) 104² - 16
= 104² - 4²
= (104 - 4)(104 + 4)
= 100.108
= 10800
b) 9⁸.2⁸ - (18⁴ - 1)(18⁴ + 1)
= 18⁸ - (18⁸ - 1)
= 18⁸ - 18⁸ + 1
= 1
c) 999³ + 3.999² + 3.999 + 1
= (999 + 1)³
= 1000³
= 1000000000
d) 42³ - 6.42² + 12.42 - 8
= (42 - 2)³
= 40³
= 64000
Bài 2
a) x(x - 2012) - 2013x + 2012.2013 = 0
⇔ x(x - 2012) - 2013(x - 2012) = 0
⇔ (x - 2012)(x - 2013) = 0
⇔ x - 2012 = 0 hoặc x - 2013 = 0
*) x - 2012 = 0
⇔ x = 2012
*) x - 2013 = 0
⇔ x = 2013
Vậy x = 2012; x = 2013
b) (x - 1)³ + 1 + 3x(x - 4) = 0
⇔ x³ - 3x² + 3x - 1 + 1 + 3x² - 12x = 0
⇔ x³ - 9x = 0
⇔ x(x² - 9) = 0
⇔ x(x - 3)(x + 3) = 0
⇔ x = 0 hoặc x - 3 = 0 hoặc x + 3 = 0
*) x - 3 = 0
⇔ x = 3
*) x + 3 = 0
⇔ x = -3
Vậy x = -3; x = 0; x = 3
c) (x + 4)² - 16 = 0
⇔ (x + 4)² - 4² = 0
⇔ (x + 4 - 4)(x + 4 + 4) = 0x
⇔ (x + 8) = 0
⇔ x = 0 hoặc x + 8 = 0
*) x + 8 = 0
⇔ x = -8
Vậy x = -8; x = 0
