To solve the expression [tex]\((b - m)(c - n) + 4a^2\)[/tex], let's break it down step-by-step and simplify the given components.
1. Identify the individual terms:
- [tex]\((b - m)\)[/tex]
- [tex]\((c - n)\)[/tex]
- [tex]\(4a^2\)[/tex]
2. Multiply the first two terms:
- When multiplying [tex]\((b - m)\)[/tex] by [tex]\((c - n)\)[/tex], use the distributive property (also known as the FOIL method for binomials):
[tex]\[
(b - m)(c - n) = b(c - n) - m(c - n)
\][/tex]
- This expands to:
[tex]\[
(b - m)(c - n) = bc - bn - mc + mn
\][/tex]
- So, simplifying it further, you get:
[tex]\[
(b - m)(c - n) = bc - bn - mc + mn
\][/tex]
3. Add the squared term:
- The term [tex]\(4a^2\)[/tex] remains as it is. Now, combine the simplified expression from step 2 with this term:
[tex]\[
(b - m)(c - n) + 4a^2 = (bc - bn - mc + mn) + 4a^2
\][/tex]
Hence, after combining all the terms, the final expression is:
[tex]\[
(b - m)(c - n) + 4a^2 = bc - bn - mc + mn + 4a^2
\][/tex]
This simplifies our given expression completely.
