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

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UpStudy AI · Accepted Answer

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

$$
13y^{2}.
$$
Результат равен $$13y^{2}$$.

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