Are the expressions A = m(2−m) and B = m(-m+2) algebraically equivalent?

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

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?

Substitute $m=3$ into expression A.

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

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

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.

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

The multiplied-out expression A is $\boxed{2m - m^2}$.

1.1.4 Multiply out expression B.

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

The multiplied-out expression B is $\boxed{-m^2 + 2m}$.

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 $-m^2 + 2m$.