Question

True or false: When you find the product of (m-n) (m-n), the middle terms have a sum of zero

since they are a zero pair.
A. True
B. False

Answer 1

A. True

(m - n) (m - n) = m(m - n) - n(m - n)

Expanding the expression, we get:

(m - n) (m - n) = m^2 - mn - mn + n^2

Simplifying the middle terms, we get:

(m - n) (m - n) = m^2 - 2mn + n^2

We can see that the middle terms, -2mn, have a sum of zero since they are opposites, or a zero pair. Therefore, the statement "the middle terms have a sum of zero" is true

Answer 2

True

Explanation:

`(m - n) \: (m - n)`

`m { \: }^(2) - mn - mn + n {}^(2)`

`m {}^(2) + n {}^(2)`

the mn has been cancelled and it's now zero