1) \(64+48x+12x^2+x^3\)
\(=4^3+3\cdot4^2\cdot x+3\cdot4\cdot x^2+x^3\)
\(=\left(4+x\right)^3\)
2) \(\dfrac{8}{27}+\dfrac{8}{3}x^2y+8xy^2+8y^3\)
\(=\left(\dfrac{2}{3}x\right)^3+3\cdot\left(\dfrac{2}{3}x\right)^2\cdot2y+3\cdot\dfrac{2}{3}\cdot\left(2y\right)^2+\left(2y\right)^3\)
\(=\left(\dfrac{2}{3}x+2y\right)^3\)
3) \(8x^6-12x^4+6x^2-1\)
\(=\left(2x^2\right)^3-3\cdot\left(2x^2\right)^2\cdot1+3\cdot2x^2\cdot1^2-1^3\)
\(=\left(2x^2-1\right)^3\)
4) \(x^3-9x^2+27x-27\)
\(=x^3-3\cdot3\cdot x^2+3\cdot3^2\cdot x-3^3\)
\(=\left(x-3\right)^3\)
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