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: 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 A and B yield the same value when m=1. 1.1.2 Choose another value for m, and substitute in A and B. Do you get the same answer? Step 1: Choose m=3. Substitute m=3 into expression A. A = m(2-m) = 3(2-3) = 3(-1) = -3 Step 2: Substitute m=3 into expression B. B = m(-m+2) = 3(-3+2) = 3(-1) = -3 Do you get the same answer? Yes Conclusion: The expressions A and B yield the same value when m=3. 1.1.3 Multiply out expression A. Step 1: Apply the distributive property to expression A. A = m(2-m) = m · 2 - m · m = 2m - m^2 The multiplied-out expression A is 2m - m^2. 1.1.4 Multiply out expression B. Step 1: Apply the distributive property to expression B. B = m(-m+2) = m · (-m) + m · 2 = -m^2 + 2m The multiplied-out expression B is -m^2 + 2m. 1.1.5 Are the multiplied-out expressions the same? Explain. Are the multiplied-out expressions the same? Yes Explain: The multiplied-out expressions 2m - m^2 and -m^2 + 2m are the same. This is because the order of terms in an addition or subtraction does not change the value of the expression (commutative property of addition). 2m - m^2 can be rewritten as -m^2 + 2m. Send me the next one 📸