Certainly! Let's simplify and evaluate the given expression step-by-step:
[tex]\[
3y(2y - 7) - 3(y - 4) - 63 \text{ for } y = -2.
\][/tex]
### Step 1: Substitute [tex]\( y = -2 \)[/tex] into the expression
First, substitute [tex]\( y = -2 \)[/tex] into the expression:
[tex]\[
3(-2)(2(-2) - 7) - 3(-2 - 4) - 63
\][/tex]
### Step 2: Simplify inside the parentheses
Evaluate inside the inner parentheses for each part of the expression:
[tex]\[
= 3(-2)[2(-2) - 7] - 3(-2 - 4) - 63
\][/tex]
[tex]\[
= 3(-2)[-4 - 7] - 3(-2 - 4) - 63
\][/tex]
[tex]\[
= 3(-2)[-11] - 3(-6) - 63
\][/tex]
### Step 3: Simplify the multiplications
Now, simplify the multiplications:
[tex]\[
= 3(-2) \times (-11) - 3 \times (-6) - 63
\][/tex]
[tex]\[
= (3 \times -2 \times -11) - (3 \times -6) - 63
\][/tex]
[tex]\[
= 66 + 18 - 63
\][/tex]
### Step 4: Combine all terms
Finally, add and subtract the simplified terms:
[tex]\[
66 + 18 - 63
\][/tex]
[tex]\[
= 21
\][/tex]
### Step 5: Present the final result
Therefore, the simplified value of the expression [tex]\(3y(2y - 7) - 3(y - 4) - 63\)[/tex] for [tex]\( y = -2 \)[/tex] is:
[tex]\[
\boxed{21}
\][/tex]
So, after breaking it down step by step, we get the final answer as [tex]\( 21 \)[/tex].
