(m+n)(m-n+1)-(m-n)(m+n-1)

2 min read Jun 16, 2024
(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

  • (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
  • (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 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.

Related Post


Featured Posts