in 1-3 sentences explain: Use the Distributive Property to prove that these algebraic expressions are equivalent. Explain your answer in one sentence for each expression and show your work:

Question

in 1-3 sentences explain:  Use the Distributive Property to prove that these algebraic expressions are equivalent. Explain your answer in one sentence for each expression and show your work:
Expression 1: (x−5)(x+3) 
Expression 2: 2x^2−x^2−2x−20+5

GPT-4o mini · Answer

To prove that the expressions $(x−5)(x+3)$ and $2x^2−x^2−2x−20+5$ are equivalent, we can simplify both expressions. **For Expression 1**: Using the Distributive Property, we have: $$ (x−5)(x+3) = x^2 + 3x - 5x - 15 = x^2 - 2x - 15. $$ **For Expression 2**: Now simplify it: $$ 2x^2 - x^2 - 2x - 20 + 5 = (2x^2 - x^2) - 2x - 20 + 5 = x^2 - 2x - 15. $$ Since both expressions simplify to $x^2 - 2x - 15$, they are equivalent.