To find the value of the expression [tex]\(36x - 8y^2\)[/tex] when [tex]\(x = 3\)[/tex] and [tex]\(y = -6\)[/tex], follow these steps:
1. Substitute the value of [tex]\(x = 3\)[/tex] into the expression:
[tex]\[
36 \times 3 - 8y^2
\][/tex]
2. Simplify the multiplication:
[tex]\[
108 - 8y^2
\][/tex]
3. Next, substitute the value of [tex]\(y = -6\)[/tex] into the expression:
[tex]\[
108 - 8 \times (-6)^2
\][/tex]
4. Calculate [tex]\((-6)^2\)[/tex]:
[tex]\[
(-6)^2 = 36
\][/tex]
5. Substitute [tex]\(36\)[/tex] back into the expression:
[tex]\[
108 - 8 \times 36
\][/tex]
6. Perform the multiplication:
[tex]\[
108 - 288
\][/tex]
7. Finally, subtract [tex]\(288\)[/tex] from [tex]\(108\)[/tex]:
[tex]\[
108 - 288 = -180
\][/tex]
Thus, the value of [tex]\(36x - 8y^2\)[/tex] when [tex]\(x = 3\)[/tex] and [tex]\(y = -6\)[/tex] is [tex]\(-180\)[/tex].
The correct answer is [tex]\( \boxed{-180} \)[/tex].
