Certainly! Let's simplify the given expression step-by-step.
We start with:
[tex]\[ 6 \sqrt{a} - 2 \sqrt{b} - \sqrt{a} - 8 \sqrt{b} \][/tex]
1. Group like terms:
Combine the terms that involve [tex]\(\sqrt{a}\)[/tex] and the terms that involve [tex]\(\sqrt{b}\)[/tex]:
[tex]\[ (6 \sqrt{a} - \sqrt{a}) + (-2 \sqrt{b} - 8 \sqrt{b}) \][/tex]
2. Simplify within the parentheses:
For the [tex]\(\sqrt{a}\)[/tex] terms:
[tex]\[ 6 \sqrt{a} - \sqrt{a} = 5 \sqrt{a} \][/tex]
For the [tex]\(\sqrt{b}\)[/tex] terms:
[tex]\[ -2 \sqrt{b} - 8 \sqrt{b} = -10 \sqrt{b} \][/tex]
3. Combine the simplified terms:
[tex]\[ 5 \sqrt{a} - 10 \sqrt{b} \][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[ 5 \sqrt{a} - 10 \sqrt{b} \][/tex]
