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.
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Here are the solutions to the questions, ensuring all formatting requirements are met: 1.1.1 Substitute m=1 in A and B respectively. Step 1: Substitute m=1 into expression A. A = m(2-m) = 1(2-1) = 1(1) = 1 Step 2: Substitute m=1 into expression B. B = m(-m+2) = 1(-1+2) = 1(1) = 1 Do you get the same answer? Yes. Conclusion: The expressions yield the same value when m=1. 1.1.2 Choose another value for m, and substitute in A and B. Step 1: Choose m=3 and substitute into expression A. A = m(2-m) = 3(2-3) = 3(-1) = -3 Step 2: Choose m=3 and substitute into expression B. B = m(-m+2) = 3(-3+2) = 3(-1) = -3 Do you get the same answer? Yes. Conclusion: The expressions yield the same value when m=3. 1.1.3 Multiply out expression A. Step 1: Distribute m into the parenthesis. A = m(2-m) = 2m - m^2 1.1.4 Multiply out expression B. Step 1: Distribute m into the parenthesis. B = m(-m+2) = -m^2 + 2m 1.1.5 Are the multiplied-out expressions the same? Explain. Yes, the multiplied-out expressions are the same. Explanation: The terms 2m and -m^2 are present in both expressions, just in a different order. This demonstrates the commutative property of addition, where a+b = b+a. 1.2.1 Substitute p=1 in C and D respectively. Step 1: Substitute p=1 into expression C. C = 3(p-2) = 3(1-2) = 3(-1) = -3 Step 2: Substitute p=1 into expression D. D = 3(2-p) = 3(2-1) = 3(1) = 3 Do you get the same answer? No. Conclusion: The expressions yield different values when p=1. That's 2 down. 3 left today — send the next one.