Answer
$2x(x+2)^2$
Work Step by Step
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
Hence here: $2x^3+8x^2+8x=2x(x^2+4x+4)=2x(x^2+2\cdot x\cdot2+1^2)=2x(x+2)^2$
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