To factor the expression \(-81y^8 - 27y^6\):
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Find the GCF (Greatest Common Factor):
- The coefficients are \(-81\) and \(-27\). The GCF of \(81\) and \(27\) is \(27\).
- The variable part has \(y^8\) and \(y^6\). The GCF for \(y^8\) and \(y^6\) is \(y^6\).
- Therefore, the GCF of the entire expression is \(27y^6\).
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Factor out the GCF: \[ -81y^8 - 27y^6 = -27y^6(3y^2 + 1) \]
Here’s how it breaks down:
- When factoring out \(27y^6\) from \(-81y^8\): \[ \frac{-81y^8}{27y^6} = -3y^2 \]
- When factoring out \(27y^6\) from \(-27y^6\): \[ \frac{-27y^6}{27y^6} = -1 \] Thus, inside the parentheses, we have: \[ -3y^2 - 1 \quad \text{can be rewritten as} \quad 3y^2 + 1 \text{ when factoring out a negative sign.} \]
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So, the final factored form is: \[ -27y^6(3y^2 + 1) \]
Therefore, the answers are:
- GCF: \(27y^6\)
- Factored Form: \(-27y^6(3y^2 + 1)\)
1 answer