Simplifying the Expression: (m+n)(mn+1)(mn)(m+n1)
This article explores the process of simplifying the expression (m+n)(mn+1)(mn)(m+n1).
Understanding the Expression
The expression involves two sets of multiplications and a subtraction. We can simplify it by expanding the brackets and then combining like terms.
Expanding the Brackets

(m+n)(mn+1): This is the product of two binomials. We can apply the distributive property (or FOIL method) to expand it:
 m(mn+1) + n(mn+1)
 m²  mn + m + mn  n² + n
 m²  n² + m + n

(mn)(m+n1): Similarly, we expand this product:
 m(m+n1)  n(m+n1)
 m² + mn  m  mn  n² + n
 m²  n²  m + n
Combining Like Terms
Now we substitute the expanded expressions back into the original expression:
(m²  n² + m + n)  (m²  n²  m + n)
We can see that both m² and n² appear in both sets of brackets with opposite signs. Therefore, they will cancel each other out when we subtract. Similarly, m and n also cancel out.
This leaves us with:
(m²  n² + m + n)  (m²  n²  m + n) = 0
Conclusion
By simplifying the expression (m+n)(mn+1)(mn)(m+n1), we find that it simplifies to 0. This means the expression has a value of zero regardless of the values of m and n.