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Verify that the expressions m(2-m) and m(-m+2) are equivalent by substituting values for m and by multiplying them out.

Mathematics

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1.1.1 Substitute m=1m=1 in A and B respectively.

  1. Substitute m=1m=1 into expression A.

    A=m(2−m)=1(2−1)=1(1)=1A = m(2-m) = 1(2-1) = 1(1) = \boxed{1}
  2. Substitute m=1m=1 into expression B.

    B=m(−m+2)=1(−1+2)=1(1)=1B = m(-m+2) = 1(-1+2) = 1(1) = \boxed{1}

    Do you get the same answer? Yes.
    Conclusion: The expressions yield the same value when m=1m=1.

    1.1.2 Choose another value for mm, and substitute in A and B.

  3. Choose m=3m=3 and substitute into expression A.

    A=m(2−m)=3(2−3)=3(−1)=−3A = m(2-m) = 3(2-3) = 3(-1) = \boxed{-3}
  4. Choose m=3m=3 and substitute into expression B.

    B=m(−m+2)=3(−3+2)=3(−1)=−3B = m(-m+2) = 3(-3+2) = 3(-1) = \boxed{-3}

    Do you get the same answer? Yes.
    Conclusion: The expressions yield the same value when m=3m=3.

    1.1.3 Multiply out expression A.

  5. Distribute mm into the parenthesis.

    A=m(2−m)=2m−m2A = m(2-m) = \boxed{2m - m^2}

    1.1.4 Multiply out expression B.

  6. Distribute mm into the parenthesis.

    B=m(−m+2)=−m2+2mB = m(-m+2) = \boxed{-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 2m2m and −m2-m^2 are present in both expressions, just in a different order. This demonstrates the commutative property of addition, where a+b=b+aa+b = b+a.

    1.2.1 Substitute p=1p=1 in C and D respectively.

  7. Substitute p=1p=1 into expression C.

    C=3(p−2)=3(1−2)=3(−1)=−3C = 3(p-2) = 3(1-2) = 3(-1) = \boxed{-3}
  8. Substitute p=1p=1 into expression D.

    D=3(2−p)=3(2−1)=3(1)=3D = 3(2-p) = 3(2-1) = 3(1) = \boxed{3}

    Do you get the same answer? No.
    Conclusion: The expressions yield different values when p=1p=1.

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