To factor the expression \(-36y^9 - 12y^7\) using the greatest common factor (GCF) of \(12y^7\), we can follow these steps:
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Identify the GCF: In this case, the GCF is \(12y^7\).
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Divide each term by the GCF:
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For the first term: \[ \frac{-36y^9}{12y^7} = -3y^{9-7} = -3y^2 \]
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For the second term: \[ \frac{-12y^7}{12y^7} = -1 \]
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Combine these results as follows: \[ -3y^2 - 1 \]
Putting it all together, you can write the factored form as:
\[ 12y^7(-3y^2 - 1) \]
So, the factored form of \(-36y^9 - 12y^7\) is: \[ 12y^7(-3y^2 - 1) \]