Show that expressions A and B are equivalent. Then show that expressions C and D are not.

Here are the solutions to the questions:

1.1.1 Substitute $m=1$ in A and B respectively.
For A:

$$m(2-m) = 1(2-1) = 1(1) = 1$$

For 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.
Let $m=3$.
For A:

$$m(2-m) = 3(2-3) = 3(-1) = -3$$

For 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.

$$A = m(2-m) = 2m - m^2$$

1.1.4 Multiply out expression B.

$$B = m(-m+2) = -m^2 + 2m$$

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.
For C:

$$3(p-2) = 3(1-2) = 3(-1) = -3$$

For D:

$$3(2-p) = 3(2-1) = 3(1) = 3$$

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