To simplify the expression \(-7 \sqrt{33} + 10 \sqrt{132}\), we first simplify \(\sqrt{132}\).
We can factor \(132\) as follows: \[ 132 = 4 \times 33 \] Taking the square root of \(132\), we have: \[ \sqrt{132} = \sqrt{4 \times 33} = \sqrt{4} \times \sqrt{33} = 2 \sqrt{33} \]
Now we substitute \(\sqrt{132}\) back into the expression: \[ -7 \sqrt{33} + 10 \sqrt{132} = -7 \sqrt{33} + 10(2 \sqrt{33}) \] This simplifies to: \[ -7 \sqrt{33} + 20 \sqrt{33} \]
Now, we combine the like terms: \[ (-7 + 20) \sqrt{33} = 13 \sqrt{33} \]
Thus, the simplified expression is: \[ \boxed{13 \sqrt{33}} \]