This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
here are the solutions to the questions: QUESTION 1 What does rs + 2 mean? Step 1: Interpret the term rs. In algebra, when two variables are written next to each other, it implies multiplication. So, rs means r × s. Step 2: Interpret the entire expression rs + 2. This means that after multiplying r by s, you then add 2 to the result. Comparing this to the options: A. Multiply r and s by 2 (Incorrect, this would be 2rs or 2(r+s)) B. Add r to s, then add 2 (Incorrect, this would be (r+s)+2) C. Multiply r by s, then add 2 (Correct) D. Add 2 to s, then multiply by r (Incorrect, this would be r(s+2)) The correct option is C. Multiply r by s, then add 2. QUESTION 2 Simplify: 3p^2 + 2p + 2p^2 + p? Step 1: Identify and group like terms. Like terms have the same variable(s) raised to the same power. The terms with p^2 are 3p^2 and 2p^2. The terms with p are 2p and p (which is 1p). Step 2: Combine the like terms. For the p^2 terms: 3p^2 + 2p^2 = (3+2)p^2 = 5p^2 For the p terms: 2p + p = (2+1)p = 3p Step 3: Write the simplified expression by combining the results from Step 2. 5p^2 + 3p Comparing this to the options: A. 8p^2 (Incorrect) B. 8p^6 (Incorrect) C. 5p^2 + 3p (Correct) D. 7p^2 + p (Incorrect) The correct option is C. 5p^2 + 3p. What's next?