1a) (t² - 9)² - (t + 3)(t - 3)(t² + 9)
= t⁴ - 18t² + 81 - (t² - 9)(t² + 9)
= t⁴ - 18t² + 81 - (t⁴ - 81)
= t⁴ - 18t² + 81 - t⁴ + 81
= -18t² + 162
b) (x² + x - 3)(x² - x + 3)
= x⁴ - (x - 3)²
= x⁴ - (x² - 6x + 9)
= x⁴ - x² + 6x - 9
2a) (-x² + 2xy - y²)/(x² - xy)
= -(x² - 2xy + y²)/x(x - y)
= -(x - y)²/x(x - y)
= (y - x)/x
b) (x⁴ - 1)/(2x - 2)
= (x² - 1)(x² + 1)/(2x - 2)
= (x - 1)(x + 1)(x² + 1)/[2(x - 1)]
= (x + 1)(x² + 1)/2
3)
a) 3x² - 2x - 1 = 0
x² + 2x² - 2x - 1 = 0
(x² - 1) + (2x² - 2x) = 0
(x - 1)(x + 1) + 2x(x - 1) = 0
(x - 1)(x + 1 + 2x) = 0
(x - 1)(3x + 1) = 0
x - 1 = 0 hoặc 3x + 1 = 0
*) x - 1 = 0
x = 1
*) 3x + 1 = 0
3x = -1
x = -1/3
Vậy x = -1/3; x = 1
b) (x + 1)/3 + (2x + 3)/5 = 3/4
20(x + 1) + 12(2x + 3) = 15.3
20x + 20 + 24x + 36 = 45
44x + 56 = 45
44x = 101
x = 101/44
4)
a³ + b³ + c³ - 3abc
= a³ + 3ab(a + b) + b³ + c³ - 3abc - 3ab(a + b)
= (a + b)³ + c³ - 3ab(a + b + c)
= (a + b + c)(a² + 2ab + b² - ac - bc + c²) - 3ab(a + b + c)
= (a + b + c)(a² + b² + c² - ab - ac - bc)
