Question
\( 1 \leftarrow \quad \begin{array}{l}5 y^{2}(2 y+5)(y-6) \\ \\ \begin{array}{l}5 y^{2}(2 y+5)(y-6)=\square \\ (\text { Simplify your answer. })\end{array}\end{array} \)
Ask by Mann Mathis. in the United Arab Emirates
Mar 16,2025
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Tutor-Verified Answer
Answer
The simplified expression is \(10y^{4}-35y^{3}-150y^{2}\).
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The Deep Dive
To simplify the expression \( 5y^2(2y + 5)(y - 6) \), start by expanding the binomials. First, multiply \( (2y + 5)(y - 6) \): \[ (2y + 5)(y - 6) = 2y^2 - 12y + 5y - 30 = 2y^2 - 7y - 30 \] Now, multiply this result by \( 5y^2 \): \[ 5y^2(2y^2 - 7y - 30) = 10y^4 - 35y^3 - 150y^2 \] So, the simplified expression is: \[ 10y^4 - 35y^3 - 150y^2 \]