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z\left(z+2y+z\right)
Factor out z.
2y+2z
Consider z+2y+z. Multiply and combine like terms.
2\left(y+z\right)
Consider 2y+2z. Factor out 2.
2z\left(y+z\right)
Rewrite the complete factored expression.
2z^{2}+2yz
Combine z^{2} and z^{2} to get 2z^{2}.