You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
In our daily life, we often use passwords, such as when making payments through Alipay. There is a type of password generated using the "factorization" method, which is easy to remember. The principle is to factorize a polynomial. For example, the polynomial $x^{3}+2x^{2}-x-2$ can be factorized as $\left(x-1\right)\left(x+1\right)\left(x+2\right)$. When $x=29$, $x-1=28$, $x+1=30$, $x+2=31$, and the numerical password obtained is $283031$.<br/>$(1)$ According to the above method, when $x=15$ and $y=5$, for the polynomial $x^{3}-xy^{2}$, after factorization, what numerical passwords can be formed?<br/>$(2)$ Given a right-angled triangle with a perimeter of $24$, a hypotenuse of $11$, and the two legs being $x$ and $y$, find a numerical password obtained by factorizing the polynomial $x^{3}y+xy^{3}$ (only one is needed).
user
24121
rule
In our daily life, we often use passwords, such as when making payments through Alipay. There is a type of password generated using the "factorization" method, which is easy to remember. The principle is to factorize a polynomial. For example, the polynomial $x^{3}+2x^{2}-x-2$ can be factorized as $\left(x-1\right)\left(x+1\right)\left(x+2\right)$. When $x=29$, $x-1=28$, $x+1=30$, $x+2=31$, and the numerical password obtained is $283031$.<br/>$(1)$ According to the above method, when $x=15$ and $y=5$, for the polynomial $x^{3}-xy^{2}$, after factorization, what numerical passwords can be formed?<br/>$(2)$ Given a right-angled triangle with a perimeter of $24$, a hypotenuse of $11$, and the two legs being $x$ and $y$, find a numerical password obtained by factorizing the polynomial $x^{3}y+xy^{3}$ (only one is needed).
train