Giải thích các bước giải:

$\begin{aligned} & \text{a) } A = (2 - x)(2 + x) - (x + 3)^2 \quad \text{tại } x = 5 \\ & A = (2^2 - x^2) - (x^2 + 6x + 9) \\ & \phantom{A} = 4 - x^2 - x^2 - 6x - 9 \\ & \phantom{A} = -2x^2 - 6x - 5 \\ & \text{Thay } x = 5: \\ & A = -2(5)^2 - 6(5) - 5 \\ & \phantom{A} = -2(25) - 30 - 5 \\ & \phantom{A} = -50 - 30 - 5 \\ & A = -85 \\ \\ & \text{b) } B = (2x + 5)^2 - 4(x - 3)(3 + x) \quad \text{tại } x = \dfrac{1}{10} \\ & B = (4x^2 + 20x + 25) - 4(x^2 - 9) \\ & \phantom{B} = 4x^2 + 20x + 25 - 4x^2 + 36 \\ & \phantom{B} = 20x + 61 \\ & \text{Thay } x = 0,1: \\ & B = 20(0,1) + 61 \\ & \phantom{B} = 2 + 61 \\ & B = 63 \\ \\ & \text{c) } C = x^3 - 3x^2 + 3x + 2023 \quad \text{tại } x = 101 \\ & C = (x^3 - 3x^2 + 3x - 1) + 1 + 2023 \\ & \phantom{C} = (x - 1)^3 + 2024 \\ & \text{Thay } x = 101: \\ & C = (101 - 1)^3 + 2024 \\ & \phantom{C} = 100^3 + 2024 \\ & \phantom{C} = 1000000 + 2024 \\ & C = 1002024 \\ \\ & \text{d) } D = x^3 - 6x^2 + 12x - 100 \quad \text{tại } x = -98 \\ & D = (x^3 - 3 \cdot x^2 \cdot 2 + 3 \cdot x \cdot 2^2 - 2^3) - 92 \\ & \phantom{D} = (x - 2)^3 - 92 \\ & \text{Thay } x = -98: \\ & D = (-98 - 2)^3 - 92 \\ & \phantom{D} = (-100)^3 - 92 \\ & \phantom{D} = -1000000 - 92 \\ & D = -1000092 \\ \\ & \text{e) } E = (x + 1)^3 + 6(x + 1)^2 + 12x + 20 \quad \text{tại } x = 5 \\ & E = (x + 1)^3+6(x+1)^2+12(x+1)+8=(x+1+2)^3=(x+3)^3 \\ & \text{Thay } x = 5: \\ & E =(5+3)^3=8^3 \\ \\ & \text{f) } F = (2x - 1)(4x^2 + 2x + 1) - 7(x^3 + 1) \quad \text{tại } x = -\dfrac{1}{2} \\ & F = ((2x)^3 - 1^3) - 7x^3 - 7 \\ & \phantom{F} = 8x^3 - 1 - 7x^3 - 7 \\ & \phantom{F} = x^3 - 8 \\ & \text{Thay } x = -0,5: \\ & F = (-0,5)^3 - 8 \\ & \phantom{F} = -0,125 - 8 \\ & F = -8,125 \\ \\ & \text{g) } G = (-x - 2)^3 + (2x - 4)(x^2 + 2x + 4) - x^2(x - 6) \quad \text{tại } x = -2 \\ & G = -(x + 2)^3 + 2(x - 2)(x^2 + 2x + 4) - (x^3 - 6x^2) \\ & \phantom{G} = -(x^3 + 6x^2 + 12x + 8) + 2(x^3 - 8) - x^3 + 6x^2 \\ & \phantom{G} = -x^3 - 6x^2 - 12x - 8 + 2x^3 - 16 - x^3 + 6x^2 \\ & \phantom{G} = (-x^3 + 2x^3 - x^3) + (-6x^2 + 6x^2) - 12x + (-8 - 16) \\ & \phantom{G} = -12x - 24 \\ & \text{Thay } x = -2: \\ & G = -12(-2) - 24 \\ & \phantom{G} = 24 - 24 \\ & G = 0 \\ \\ & \text{h) } H = (x - 1)^3 - (x + 2)(x^2 - 2x + 4) + 3(x + 4)(x - 4) \quad \text{tại } x = -\dfrac{1}{2} \\ & H = (x^3 - 3x^2 + 3x - 1) - (x^3 + 8) + 3(x^2 - 16) \\ & \phantom{H} = x^3 - 3x^2 + 3x - 1 - x^3 - 8 + 3x^2 - 48 \\ & \phantom{H} = (x^3 - x^3) + (-3x^2 + 3x^2) + 3x + (-1 - 8 - 48) \\ & \phantom{H} = 3x - 57 \\ & \text{Thay } x = -0,5: \\ & H = 3(-0,5) - 57 \\ & \phantom{H} = -1,5 - 57 \\ & H = -58,5 \end{aligned}$