Question

Answer 1

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

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

c: \(1-9x+27x^2-27x^3=\left(1-3x\right)^3\)

d: \(x^3+\dfrac{3}{2}x^2+\dfrac{3}{4}x+\dfrac{1}{8}=\left(x+\dfrac{1}{2}\right)^3\)

e: \(27x^3-54x^2y+36xy^2-8y^3=\left(3x-2y\right)^3\)

f: \(x^2-2xy+y^2-4m^2+4mn-n^2\)

\(=\left(x-y\right)^2-\left(2m-n\right)^2\)

\(=\left(x-y-2m+n\right)\left(x-y+2m-n\right)\)