1. Problem: Simplify the expression $7y(5x+10)-(x+2)(3x+5)$. 2. Formula and rules: use the distributive property $a(b+c)=ab+ac$ and the rule for subtracting an entire expression $-(A+B+C)=-A-B-C$. 3. Expand the first product: $7y(5x+10)=35xy+70y$. 4. Expand the second product: $(x+2)(3x+5)=3x^2+11x+10$. 5. Combine the results and remove parentheses: $35xy+70y-(3x^2+11x+10)$. 6. Distribute the subtraction: $35xy+70y-3x^2-11x-10$. 7. Rearrange terms in a conventional order and state the final simplified form: $-3x^2+35xy-11x+70y-10$. 8. Explanation: we applied the distributive property to remove parentheses and combined like terms where applicable; no like terms of the same variable-degree appeared to combine further, so this is fully simplified.