ростите выражение \[ \left(y^{2}-2 y\right)^{2}-y^{2}(y+3)(y-3)+2 y\left(2 y^{2}+\right. \]

Simplify the expression by following steps: - step0: Simplify: \(\left(y^{2}-2y\right)^{2}-y^{2}\left(y+3\right)\left(y-3\right)+2y\left(2y^{2}\right)\) - step1: Multiply the terms: \(\left(y^{2}-2y\right)^{2}-y^{2}\left(y+3\right)\left(y-3\right)+2y\times 2y^{2}\) - step2: Multiply: \(\left(y^{2}-2y\right)^{2}-y^{2}\left(y+3\right)\left(y-3\right)+4y^{3}\) - step3: Expand the expression: \(y^{4}-4y^{3}+4y^{2}-y^{2}\left(y+3\right)\left(y-3\right)+4y^{3}\) - step4: Expand the expression: \(y^{4}-4y^{3}+4y^{2}-y^{4}+9y^{2}+4y^{3}\) - step5: Collect like terms: \(4y^{2}+9y^{2}\) - step6: Collect like terms: \(\left(4+9\right)y^{2}\) - step7: Add the numbers: \(13y^{2}\) Результат разложения выражения \[ \left(y^{2}-2 y\right)^{2}-y^{2}(y+3)(y-3)+2 y\left(2 y^{2}\right) \] равен \[ 13y^{2}. \]