(m-n%2B1)-(m-n)(m%2Bn-1).jpeg "(m+n)(m-n+1)-(m-n)(m+n-1)")
Simplifying the Expression: (m+n)(m-n+1)-(m-n)(m+n-1)
This article explores the process of simplifying the expression (m+n)(m-n+1)-(m-n)(m+n-1).
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
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(m+n)(m-n+1): This is the product of two binomials. We can apply the distributive property (or FOIL method) to expand it:
- m(m-n+1) + n(m-n+1)
- m² - mn + m + mn - n² + n
- m² - n² + m + n
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(m-n)(m+n-1): Similarly, we expand this product:
- m(m+n-1) - n(m+n-1)
- 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)(m-n+1)-(m-n)(m+n-1), we find that it simplifies to 0. This means the expression has a value of zero regardless of the values of m and n.