d) Ta có: \(D=x^3-3x^2+3x-1\)
\(=\left(x-1\right)^3\)
\(=\left(1001-1\right)^3=1000^3=1000000000\)
e) Ta có: \(D=\left(x+y\right)^3-9\left(x-y\right)^2+27\left(x+y\right)-27\)
\(=\left(x+y-3\right)^3\)
\(=\left(2+6-3\right)^3\)
\(=5^3=125\)
f) Ta có: \(F=27x^3z^6-54x^2yz^4+36xy^2z^2-8y^3\)
\(=\left(3xz^2\right)^3-3\cdot\left(3xz^2\right)^2\cdot2y+3\cdot3xz^2\cdot\left(2y\right)^2-\cdot\left(2y\right)^3\)
\(=\left(3xz^2-2y\right)^3\)
\(=\left(3\cdot25\cdot2^2-2\cdot150\right)^3\)
\(=0^3=0\)
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