Let's analyze and solve the problem step-by-step.
1. Define the expressions:
- Let [tex]\( A \)[/tex] be the difference between [tex]\( 4x \)[/tex] and [tex]\( 5y \)[/tex].
[tex]\[
A = 4x - 5y
\][/tex]
- Let [tex]\( B \)[/tex] be the sum of [tex]\( 4x \)[/tex] and [tex]\( 5y \)[/tex].
[tex]\[
B = 4x + 5y
\][/tex]
2. Formulate the main operation:
- We need to find the result of subtracting [tex]\( B \)[/tex] from [tex]\( A \)[/tex].
This translates to:
[tex]\[
A - B
\][/tex]
3. Substitute the expressions for [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
[tex]\[
(4x - 5y) - (4x + 5y)
\][/tex]
4. Distribute and simplify:
- First, remove the parentheses by distributing the negative sign through the second expression:
[tex]\[
4x - 5y - 4x - 5y
\][/tex]
- Notice that [tex]\( +4x \)[/tex] and [tex]\( -4x \)[/tex] cancel each other:
[tex]\[
4x - 4x - 5y - 5y = 0 - 5y - 5y = -10y
\][/tex]
Therefore, the simplified result is:
[tex]\[
-10y
\][/tex]
So, the final answer is:
[tex]\[
-10y
\][/tex]
