To find the product \(-4y^2(-4y^2 - 5)\), we will distribute \(-4y^2\) to each term inside the parentheses.
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Multiply \(-4y^2\) by \(-4y^2\): \[ -4y^2 \cdot -4y^2 = 16y^4 \]
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Multiply \(-4y^2\) by \(-5\): \[ -4y^2 \cdot -5 = 20y^2 \]
Now, we combine both results: \[ 16y^4 + 20y^2 \]
Thus, the simplified product is: \[ \boxed{16y^4 + 20y^2} \]