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Answer
The expression \( 4\pi R^{2} - 8\pi R \) can be factored as \( 4\pi R (R - 2) \).
Solution
It looks like you want to **factorise** the expression \( 4\pi R^{2} - 8\pi R \). Let's go through the steps to factorise it:
1. **Identify the Greatest Common Factor (GCF):**
Both terms \(4\pi R^{2}\) and \(8\pi R\) share common factors:
- **Numerical Coefficient:** The GCF of 4 and 8 is 4.
- **Variable Factors:** Both terms have at least one \( \pi \) and one \( R \).
So, the GCF is \(4\pi R\).
2. **Factor Out the GCF:**
Divide each term by the GCF \(4\pi R\):
\[
\begin{align*}
4\pi R^{2} - 8\pi R &= 4\pi R \left( \frac{4\pi R^{2}}{4\pi R} \right) - 4\pi R \left( \frac{8\pi R}{4\pi R} \right) \\
&= 4\pi R (R) - 4\pi R (2) \\
&= 4\pi R (R - 2)
\end{align*}
\]
3. **Final Factored Form:**
\[
4\pi R^{2} - 8\pi R = 4\pi R (R - 2)
\]
So, the factorised form of \( 4\pi R^{2} - 8\pi R \) is:
\[
4\pi R (R - 2)
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To factor the expression \( 4 \pi R^{2} - 8 \pi R \), we can start by taking out the common factors. Here, both terms have \( 4 \pi \) as a common factor: \[ 4 \pi (R^{2} - 2R) \] Now, we can further factor \( R^{2} - 2R \) as: \[ R(R - 2) \] So the entire expression can be factored as: \[ 4 \pi R(R - 2) \] And there you have it, beautifully factored!
