Question

Expression: -81y⁸-27y⁶
GCF: □
Factored Form: □

Answer 1

To factor the expression \(-81y^8 - 27y^6\):

1. **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 \(27y^6\).

2. **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:
\[
-3y^2 - 1 \quad \text{can be rewritten as} \quad 3y^2 + 1 \text{ when factoring out a negative sign.}
\]

3. **So, the final factored form is**:
\[
-27y^6(3y^2 + 1)
\]

Therefore, the answers are:

- GCF: \(27y^6\)
- Factored Form: \(-27y^6(3y^2 + 1)\)