c: \(8x^3+12x^2y+6xy^2+y^3\)
\(=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot y+3\cdot2x\cdot y^2+y^3\)
\(=\left(2x+y\right)^3\)
d: \(-x^3+9x^2-27x+27\)
\(=3^3-3\cdot3^2\cdot x+3\cdot3\cdot x^2-x^3\)
\(=\left(3-x\right)^3\)
e: \(x^3+\dfrac{1}{27}\)
\(=x^3+\left(\dfrac{1}{3}\right)^3\)
\(=\left(x+\dfrac{1}{3}\right)\left(x^2-\dfrac{1}{3}x+\dfrac{1}{9}\right)\)
g: \(\dfrac{1}{25}x^2-64y^2\)
\(=\left(\dfrac{1}{5}x\right)^2-\left(8y\right)^2\)
\(=\left(\dfrac{1}{5}x-8y\right)\left(\dfrac{1}{5}x+8y\right)\)
\(c)8x^3+12x^2y+6xy^2+y^2=(2x+y)^3 \)
\(d)-x^3+9x^2-27x+27=3^3-9x^2+27x-x^3=(3-x)^3\)
\(e)\)\(x^3+\dfrac{1}{27}=x^3+\left(\dfrac{1}{3}\right)^3=\left(x+\dfrac{1}{3}\right)\left(x^2-\dfrac{1}{3}x+\dfrac{1}{9}\right)\)
\(g)\)\(\dfrac{1}{25}x^2-64y^2=\left(\dfrac{1}{5}+8y\right)\left(\dfrac{1}{5}-8y\right)\)
