Sure, let's simplify the given expression step by step:
The expression is:
[tex]\[ -4(-8w - 4x) - 7x - 10(-10x + 8w) \][/tex]
First, let's distribute the constants inside the parentheses:
[tex]\[ -4(-8w) - 4(-4x) - 7x - 10(-10x) - 10(8w) \][/tex]
This results in:
[tex]\[ 32w + 16x - 7x + 100x - 80w \][/tex]
Now, let's combine like terms. We'll group the terms with [tex]\(w\)[/tex] together and the terms with [tex]\(x\)[/tex] together:
For [tex]\(w\)[/tex]:
[tex]\[ 32w - 80w = -48w \][/tex]
For [tex]\(x\)[/tex]:
[tex]\[ 16x - 7x + 100x = 109x \][/tex]
Thus, the simplified expression is:
[tex]\[ -48w + 109x \][/tex]
So, the simplest form of the expression [tex]\( -4(-8 w-4 x)-7 x-10(-10 x+8 w) \)[/tex] is:
[tex]\[ \boxed{-48w + 109x} \][/tex]
