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