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4\left(xy^{2}+8xy+16x\right)
Factor out 4.
x\left(y^{2}+8y+16\right)
Consider xy^{2}+8xy+16x. Factor out x.
\left(y+4\right)^{2}
Consider y^{2}+8y+16. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=y and b=4.
4x\left(y+4\right)^{2}
Rewrite the complete factored expression.