Match Equivalent Expressions: (m-n)(a-4) and Related Forms

To solve this problem, we'll use the distributive property to expand each expression and find its equivalent form.

**Step 1: Expand each given expression.**

• For $(m-n)(a-4)$:

$(m-n)(a-4) = m \cdot a - m \cdot 4 - n \cdot a + n \cdot 4 = ma - 4m - na + 4n$

• For $(4-n)(m+a)$:

$(4-n)(m+a) = 4 \cdot m + 4 \cdot a - n \cdot m - n \cdot a = 4m + 4a - nm - na$

• For $(n-m)(4-a)$:

$(n-m)(4-a) = n \cdot 4 - n \cdot a - m \cdot 4 + m \cdot a = 4n - na - 4m + ma = -ma + 4m + na - 4n$

**Step 2: Match expanded expressions with the given options.**

• $ma - 4m - na + 4n$ matches option b.

• $4m + 4a - nm - na$ matches option a.

• $-ma + 4m + na - 4n$ matches option c.

The expanded expressions match the options as follows:

• Expression $(m-n)(a-4)$ matches option b.

• Expression $(4-n)(m+a)$ matches option a.

• Expression $(n-m)(4-a)$ matches option c.

Thus, the correct matches are 1-b, 2-a, 3-c.