d: \(D=x^3-6x^2+12x-100\)

\(=x^3-6x^2+12x-8-92\)

\(=\left(x-2\right)^3-92\)

Khi x=-98 thì \(D=\left(-98-2\right)^3-92=-1000000-92=-1000092\)

e: \(E=\left(x+1\right)^3+6\left(x+1\right)^2+12x+20\)

\(=\left(x+1\right)^3+6\left(x+1\right)^2+12\left(x+1\right)+8\)

\(=\left(x+1+2\right)^3\)

\(=\left(x+3\right)^3\)

Khi x=5 thì \(E=\left(5+3\right)^3=8^3=512\)

f: \(F=\left(2x-1\right)\left(4x^2+2x+1\right)-7\left(x^3+1\right)\)

\(=\left(2x\right)^3-1^3-7x^3-7\)

\(=x^3-8\)

Khi x=-1/2 thì \(F=\left(-\dfrac{1}{2}\right)^3-8=-\dfrac{1}{8}-8=-\dfrac{65}{8}\)

g: \(G=\left(-x-2\right)^3+\left(2x-4\right)\left(x^2+2x+4\right)-x^2\left(x-6\right)\)

\(=-\left(x+2\right)^3+2\left(x-2\right)\left(x^2+2x+4\right)-x^3+6x^2\)

\(=-x^3-6x^2-12x-8+2\left(x^3-8\right)-x^3+6x^2\)

\(=-2x^3-12x-8+2x^3-16=-12x-24\)

Khi x=-2 thì \(G=-12\cdot\left(-2\right)-24=24-24=0\)

h: \(H=\left(x-1\right)^3-\left(x+2\right)\left(x^2-2x+4\right)+3\left(x+4\right)\left(x-4\right)\)

\(=x^3-3x^2+3x-1-\left(x^3+8\right)+3\left(x^2-16\right)\)

\(=x^3-3x^2+3x-1-x^3-8+3x^2-48\)

\(=3x-57\)

Khi x=-1/2 thì \(H=3\cdot\dfrac{-1}{2}-57=-1,5-57=-58,5\)

`@` `\text {Ans}`

`\downarrow`

`a)`

\((x+3)^2 - (x-4)(x+4)\)

`= (x^2 + 6x + 9) - (x^2 + 4x - 4x - 16)`

`= x^2 + 6x + 9 - (x^2 - 16)`

`= x^2 + 6x + 9 - x^2 + 16`

`= 6x + 25`

`b)`

\(3(x+2)^2 + (2x-1)^2 - 7(3+x)(x-3)\)

`= 3(x^2 + 4x + 4) + (4x^2 - 4x + 1) - 7(x^2 - 9)`

`= 3x^2 + 12x + 12 + 4x^2 - 4x + 1 - 7x^2 + 63`

`= (3x^2 + 4x^2 - 7x^2) + (12x - 4x) + (12 + 1 + 63)`

`= 8x + 76`

`c)`

\((x+2)^2 + (x-3)^2 - 2(x+1)(x-1)\)

`= (x^2 + 4x + 4) + (x^2 - 6x + 9) - 2(x^2 - 1)`

`= x^2 + 4x + 4 + x^2 - 6x + 9 - 2x^2 + 2`

`= (x^2 + x^2 - 2x^2) + (4x - 6x) + (4 + 9 + 2)`

`= -2x + 15`

`d)`

\((x+1)^3 - x(x-2)^2 + x - 1\)

`= (x^3 + 3x^2 + 3x + 1) - x(x^2 - 4x + 4) + x - 1`

`= x^3 + 3x^2 + 3x + 1 - x^3 + 4x^2 - 4x + x - 1`

`= (x^3 - x^3) + (3x^2 + 4x^2) + (3x - 4x + x) + (1-1)`

`= 7x^2 `

`@` `\text {Kaizuu lv uuu}`

Ta có:

Ta có:

Ta có:

Ta có:

Ta có:

Ta có: