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

Question

Join expressions of equal value

  1. (mn)(a4) (m-n)(a-4)

  2. (4n)(m+a) (4-n)(m+a)

  3. (nm)(4a) (n-m)(4-a)

    a.4m+4anmna 4m+4a-nm-na

    b.ma4mna+4n ma-4m-na+4n

    c.ma+4m+na4n -ma+4m+na-4n

Video Solution

Step-by-Step Solution

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 (mn)(a4) (m-n)(a-4) :

(mn)(a4)=mam4na+n4=ma4mna+4n (m-n)(a-4) = m \cdot a - m \cdot 4 - n \cdot a + n \cdot 4 = ma - 4m - na + 4n

  • For (4n)(m+a) (4-n)(m+a) :

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

  • For (nm)(4a) (n-m)(4-a) :

(nm)(4a)=n4nam4+ma=4nna4m+ma=ma+4m+na4n (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.**

  • ma4mna+4n ma - 4m - na + 4n matches option b.

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

  • ma+4m+na4n -ma + 4m + na - 4n matches option c.

The expanded expressions match the options as follows:

  • Expression (mn)(a4) (m-n)(a-4) matches option b.

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

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

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

Answer

1-b, 2-a, 3-c