To simplify the expression \(-7y^2(9y - 8)\), distribute \(-7y^2\) to both terms inside the parentheses:
\[ -7y^2 \cdot 9y + (-7y^2) \cdot (-8) \]
Calculating each term:
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For the first term: \[ -7y^2 \cdot 9y = -63y^3 \]
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For the second term: \[ -7y^2 \cdot -8 = 56y^2 \]
Now, combine the results:
\[ -63y^3 + 56y^2 \]
Thus, the simplified form is:
\[ \boxed{-63y^3 + 56y^2} \]