To evaluate the expression \( 3y(2y - 7) - 3(y - 4) - 63 \) for \( y = -2 \), we will follow these steps:
- Substitute \( y = -2 \) into the expression.
- Simplify the result step by step.
Start with the expression:
\[ 3y(2y - 7) - 3(y - 4) - 63 \]
Substituting \( y = -2 \):
\[ 3(-2)(2(-2) - 7) - 3(-2 - 4) - 63 \]
Now simplify inside the parentheses:
- Calculate \( 2(-2) - 7 \):
\[ 2(-2) = -4 \quad \text{so} \quad -4 - 7 = -11 \]
- Calculate \( -2 - 4 \):
\[ -2 - 4 = -6 \]
Now substitute these results back into the expression:
\[ 3(-2)(-11) - 3(-6) - 63 \]
Now calculate \( 3(-2)(-11) \):
\[ 3(-2)(-11) = 6 \cdot 11 = 66 \]
Next, calculate \( -3(-6) \):
\[ -3(-6) = 18 \]
Now put everything together:
\[ 66 + 18 - 63 \]
Simplify \( 66 + 18 = 84 \) and then:
\[ 84 - 63 = 21 \]
Thus, the final answer is:
\[ \boxed{21} \]
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