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2\left(9y^{3}+24y^{2}+16y\right)
Factor out 2.
y\left(9y^{2}+24y+16\right)
Consider 9y^{3}+24y^{2}+16y. Factor out y.
\left(3y+4\right)^{2}
Consider 9y^{2}+24y+16. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=3y and b=4.
2y\left(3y+4\right)^{2}
Rewrite the complete factored expression.