To simplify the expression [tex]\(-4r(-11r + 2r - 14)\)[/tex], we need to proceed step-by-step.
First, let's simplify the expression inside the parentheses:
[tex]\[
-11r + 2r - 14
\][/tex]
Combining like terms, we get:
[tex]\[
-11r + 2r = (-11 + 2)r = -9r
\][/tex]
Therefore, the expression inside the parentheses simplifies to:
[tex]\[
-9r - 14
\][/tex]
Next, we need to distribute [tex]\(-4r\)[/tex] through the simplified expression inside the parentheses:
[tex]\[
-4r(-9r - 14)
\][/tex]
We distribute [tex]\(-4r\)[/tex] to both terms inside the parentheses:
1. Distributing [tex]\(-4r\)[/tex] to [tex]\(-9r\)[/tex]:
[tex]\[
-4r \cdot -9r = 36r^2
\][/tex]
2. Distributing [tex]\(-4r\)[/tex] to [tex]\(-14\)[/tex]:
[tex]\[
-4r \cdot -14 = 56r
\][/tex]
Combining these results, we have:
[tex]\[
36r^2 + 56r
\][/tex]
Thus, the simplified expression is:
[tex]\[
36r^2 + 56r
\][/tex]
Therefore, the answer is:
[tex]\[
\boxed{36r^2 + 56r}
\][/tex]
