Solve (m+n)(4+?) = n²+mn+4m+4n: Find the Missing Term

Question

Complete the missing element

(m+n)(4+?)=n2+mn+4m+4n (m+n)(4+?)=n^2+mn+4m+4n

Video Solution

Step-by-Step Solution

To solve this problem, we'll apply the distributive property to expand and match the expressions:

  • Step 1: Expand (m+n)(4+?)(m+n)(4+?) using distributive property: (m+n)(4+n)=m(4+n)+n(4+n) (m+n)(4+n) = m(4+n) + n(4+n) .
  • Step 2: This gives us 4m+mn+4n+n2 4m + mn + 4n + n^2 .
  • Step 3: Compare this to the expression n2+mn+4m+4n n^2 + mn + 4m + 4n .

The expanded expression matches the target expression, so the missing term in (m+n)(4+?)(m+n)(4+?) is indeed nn.

Therefore, the complete expression is (m+n)(4+n)(m+n)(4+n).

Answer

n n