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2\left(4x^{3}+12x^{2}+9x\right)
Factor out 2.
x\left(4x^{2}+12x+9\right)
Consider 4x^{3}+12x^{2}+9x. Factor out x.
\left(2x+3\right)^{2}
Consider 4x^{2}+12x+9. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=2x and b=3.
2x\left(2x+3\right)^{2}
Rewrite the complete factored expression.