1. Stating the problem: You asked me to check the answers in a paper you will send. 2. What I need: Please upload the paper or paste the problems and your answers so I can check them step by step. 3. How I will check: I will verify arithmetic, algebraic manipulations, definitions, and final conclusions. I will check computations, show corrections, and give brief explanations for any errors. I may use formulas like $a+b=c$ for simple illustrative checks or display full calculations when needed. 4. Rules and method: I will state the relevant formula or theorem, show all intermediate steps, and explain why each step is valid. I will highlight incorrect steps, provide corrected work, and give short, learner-friendly explanations. 5. Final answer: Please attach the paper or paste the answers and I will begin checking them now.