Are the expressions m(2-m) and m(−m+2) equivalent? Explain.

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Question 2

2.1.3
Based on your observations from 2.1.1 and 2.1.2, both expressions $m(2-m)$ and $m(-m+2)$ yielded the same result when $m=1$ . This suggests that the two expressions might be equivalent.

2.1.4
Choose another value for $m$ , and substitute in A and B. Do you get the same answer?

Let's choose $m=2$ .

A) For $m(2 - m)$ :
Substitute $m=2$ :

2(2 - 2) = 2(0) = \boxed{0}

B) For $m(-m + 2)$ :
Substitute $m=2$ :

2(-2 + 2) = 2(0) = \boxed{0}

Yes, we get the same answer.

2.1.5
What is your conclusion?

Based on the calculations for $m=1$ and $m=2$ , both expressions $m(2-m)$ and $m(-m+2)$ consistently produce the same output value for the same input value of $m$ . This strongly suggests that the two expressions are equivalent.

2.1.6
Multiply out expression A.

Expression A is $m(2 - m)$ .

Apply the distributive property.
$m(2 - m) = m \times 2 - m \times m$ $m(2 - m) = \boxed{2m - m^2}$
2.1.7
Multiply out expression B.

Expression B is $m(-m + 2)$ .
Apply the distributive property.
$m(-m + 2) = m \times (-m) + m \times 2$ $m(-m + 2) = \boxed{-m^2 + 2m}$
2.1.8
Are the multiplied-out expressions the same? Explain.

Yes, the multiplied-out expressions are the same.
The expression from A is $2m - m^2$ , and the expression from B is $-m^2 + 2m$ . These are identical because the order of terms in an addition or subtraction does not change the value (commutative property of addition).

Are the expressions m(2-m) and m(-m+2) equivalent? Explain.

Step-by-step solution

Apply the distributive property.

Apply the distributive property.

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