C1
a) (x+2)² - (x-3)
Cách 1: (x+2)² - (x-3)
= (x+2)(x+2) - (x-3)
= x² + 4x + 4 - (x-3)
= x² + 4x + 4 - x + 3
= x² + 3x + 7
Cách 2: (x+2)² - (x-3)
= (x+2)(x+2) - (x-3)
= x² + 4x + 4 - (x² - 3x + 3)
= x² + 4x + 4 - x² + 3x - 3
= 7x + 1
b) (2x + 1)² - (x+4)(x+4)
Cách 1: (2x + 1)² - (x+4)(x+4)
= (2x + 1)(2x + 1) - (x+4)(x+4)
= 4x² + 4x + 1 - (x² + 8x + 16)
= 4x² + 4x + 1 - x² - 8x - 16
= 3x² - 4x - 15
Cách 2: (2x + 1)² - (x+4)(x+4)
= (2x + 1)(2x + 1) - (x+4)(x+4)
= 4x² + 4x + 1 - (x² + 8x + 16)
= 4x² + 4x + 1 - x² - 8x - 16
= 3x² - 4x - 15
c) (3x-2) - (2x-3)²
Cách 1: (3x-2) - (2x-3)²
= 3x - 2 - (2x-3)(2x-3)
= 3x - 2 - (4x² - 12x + 9)
= 3x - 2 - 4x² + 12x - 9
= -4x² + 15x - 11
Cách 2: (3x-2) - (2x-3)²
= 3x - 2 - (2x-3)(2x-3)
= 3x - 2 - (4x² - 12x + 9)
= 3x - 2 - 4x² + 12x - 9
= -4x² + 15x - 11
d) (x+3)(x²-3x+9) - (x+4)(x-3)(x+3)
Cách 1: (x+3)(x²-3x+9) - (x+4)(x-3)(x+3)
= (x³ - 3x² + 9x) - (x+4)(x-3)(x+3)
= x³ - 3x² + 9x - (x+4)(x-3)(x+3)
Cách 2: (x+3)(x²-3x+9) - (x+4)(x-3)(x+3)
= (x³ - 3x² + 9x) - (x+4)(x-3)(x+3)
= x³ - 3x² + 9x - (x+4)(x-3)(x+3)
C2
x² + 4x + 4 = (x+2)².
C3
b) 4x² + 4x + 1 = 0
a = 4, b = 4, c = 1
x = (-4 ± √(4² - 4*4*1)) / (2*4)
x = (-4 ± √(16 - 16)) / 8
x = (-4 ± √0) / 8
x = -4/8
x = -1/2
a) x² - 4x + 4 = 0
a = 1, b = -4, c = 4
x = (-(-4) ± √((-4)² - 4*1*4)) / (2*1)
x = (4 ± √(16 - 16)) / 2
x = (4 ± √0) / 2
x = 4/2
x = 2
c) x² + x + 1/4 = 0
a = 1, b = 1, c = 1/4
x = (-1 ± √(1² - 4*1*(1/4))) / (2*1)
x = (-1 ± √(1 - 1)) / 2
x = (-1 ± √0) / 2
x = -1/2
d) 9x² + 12x + 4 = 0
a = 9, b = 12, c = 4
x = (-12 ± √(12² - 4*9*4)) / (2*9)
x = (-12 ± √(144 - 144)) / 18
x = (-12 ± √0) / 18
x = -12/18
x = -2/3
e) x² + 10x + 25 = 0
a = 1, b = 10, c = 25
x = (-10 ± √(10² - 4*1*25)) / (2*1)
x = (-10 ± √(100 - 100)) / 2
x = (-10 ± √0) / 2 x = -10/2
x = -5


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