Certainly! Let's simplify the given expression step-by-step:
[tex]\[ -15 \sqrt{x} + 4 \sqrt{y} - \sqrt{x} - 7 \sqrt{y} \][/tex]
1. Group like terms:
The terms involving [tex]\(\sqrt{x}\)[/tex] are [tex]\(-15 \sqrt{x}\)[/tex] and [tex]\(-\sqrt{x}\)[/tex].
The terms involving [tex]\(\sqrt{y}\)[/tex] are [tex]\(4 \sqrt{y}\)[/tex] and [tex]\(-7 \sqrt{y}\)[/tex].
2. Combine coefficients of [tex]\(\sqrt{x}\)[/tex]:
[tex]\[
-15 \sqrt{x} - \sqrt{x} = (-15 - 1) \sqrt{x} = -16 \sqrt{x}
\][/tex]
3. Combine coefficients of [tex]\(\sqrt{y}\)[/tex]:
[tex]\[
4 \sqrt{y} - 7 \sqrt{y} = (4 - 7) \sqrt{y} = -3 \sqrt{y}
\][/tex]
4. Write the simplified expression:
Combine the results from the above steps:
[tex]\[
-16 \sqrt{x} - 3 \sqrt{y}
\][/tex]
Thus, the simplified expression is:
[tex]\[ \boxed{-16 \sqrt{x} - 3 \sqrt{y}} \][/tex]
