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2\left(xy^{2}+2xy+x\right)
Factor out 2.
x\left(y^{2}+2y+1\right)
Consider xy^{2}+2xy+x. Factor out x.
\left(y+1\right)^{2}
Consider y^{2}+2y+1. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=y and b=1.
2x\left(y+1\right)^{2}
Rewrite the complete factored expression.