Let's solve the expression step-by-step:
We are given the expression:
[tex]\[ 17 \sqrt{b} - 9 \sqrt{b} - \sqrt{b} - 6 \sqrt{b} \][/tex]
1. First, identify all the terms that involve [tex]\(\sqrt{b}\)[/tex]. Each term has [tex]\(\sqrt{b}\)[/tex] as a common factor.
2. Combine the coefficients (the numbers multiplying [tex]\(\sqrt{b}\)[/tex]) of each term.
The coefficients are:
[tex]\[ 17, -9, -1, -6 \][/tex]
3. Add these coefficients together:
[tex]\[ 17 - 9 = 8 \][/tex]
[tex]\[ 8 - 1 = 7 \][/tex]
[tex]\[ 7 - 6 = 1 \][/tex]
So the combined coefficient of [tex]\(\sqrt{b}\)[/tex] is [tex]\(1\)[/tex].
4. Now, multiply this combined coefficient by [tex]\(\sqrt{b}\)[/tex].
Therefore,
[tex]\[ 17 \sqrt{b} - 9 \sqrt{b} - \sqrt{b} - 6 \sqrt{b} = 1 \sqrt{b} \][/tex]
Simplifying, we get:
[tex]\[ 1 \sqrt{b} = \sqrt{b} \][/tex]
So the simplified expression is:
[tex]\[ \sqrt{b} \][/tex]
Therefore,
[tex]\[ 17 \sqrt{b} - 9 \sqrt{b} - \sqrt{b} - 6 \sqrt{b} = \sqrt{b} \][/tex]
