Certainly! Let's go through the process of simplifying the given expression step by step.
The expression provided is:
[tex]\[
3(-5x + 5y) + 3(-x - 4y) - 2(5x - 5y)
\][/tex]
First, let's distribute the constants (3 and -2) through their respective parentheses:
1. Distribute the 3 in the first term:
[tex]\[
3(-5x + 5y) = 3 \cdot (-5x) + 3 \cdot (5y) = -15x + 15y
\][/tex]
2. Distribute the 3 in the second term:
[tex]\[
3(-x - 4y) = 3 \cdot (-x) + 3 \cdot (-4y) = -3x - 12y
\][/tex]
3. Distribute the -2 in the third term:
[tex]\[
-2(5x - 5y) = -2 \cdot (5x) - 2 \cdot (-5y) = -10x + 10y
\][/tex]
Next, combine all the expressions:
[tex]\[
-15x + 15y + (-3x - 12y) + (-10x + 10y)
\][/tex]
Now, group the like terms together:
Combine the [tex]\(x\)[/tex]-terms:
[tex]\[
-15x - 3x - 10x = -28x
\][/tex]
Combine the [tex]\(y\)[/tex]-terms:
[tex]\[
15y - 12y + 10y = 13y
\][/tex]
So the simplified expression is:
[tex]\[
-28x + 13y
\][/tex]
Therefore, the simplest form of the expression [tex]\(3(-5x + 5y) + 3(-x - 4y) - 2(5x - 5y)\)[/tex] is:
[tex]\[
\boxed{-28x + 13y}
\][/tex]
