Certainly! Let's analyze and simplify the given expression [tex]\((m + n) \cdot (m - n)\)[/tex] step-by-step:
1. Expression Setup: We start with the expression [tex]\((m + n) \cdot (m - n)\)[/tex].
2. Applying the Distributive Property (Difference of Squares):
To simplify [tex]\((m + n) \cdot (m - n)\)[/tex], we will use the difference of squares formula, which states:
[tex]\[
(a + b)(a - b) = a^2 - b^2
\][/tex]
Here, our [tex]\(a = m\)[/tex] and [tex]\(b = n\)[/tex].
3. Substituting [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the Formula:
Using the difference of squares formula, we substitute:
[tex]\[
(m + n)(m - n) = m^2 - n^2
\][/tex]
4. Final Expression:
After applying the formula, we arrive at:
[tex]\[
(m + n)(m - n) = m^2 - n^2
\][/tex]
So, the simplified form of the expression [tex]\((m + n) \cdot (m - n)\)[/tex] is [tex]\(m^2 - n^2\)[/tex].
