factor using GCF with solution -8a²b+4ab

To factor the expression \(-8a^2b + 4ab\) using the Greatest Common Factor (GCF), follow these steps:

### Step 1: Identify the GCF of the terms.
- The terms are \(-8a^2b\) and \(4ab\).
- **Numerical coefficients:** The GCF of the numbers \(-8\) and \(4\) is \(4\).
- **Variable part:** The GCF of \(a^2b\) and \(ab\) is \(ab\) (since \(ab\) is the lowest power of \(a\) and \(b\) present in both terms).

So, the GCF of the entire expression is \(4ab\).

### Step 2: Factor out the GCF.
- Divide each term by the GCF and write the expression as a product of the GCF and the resulting expression.

\[
\begin{aligned}
-8a^2b + 4ab &= 4ab \left(\frac{-8a^2b}{4ab} + \frac{4ab}{4ab}\right) \\
&= 4ab \left(-2a + 1\right)
\end{aligned}
\]

### Final Answer:
\[
-8a^2b + 4ab = 4ab(-2a + 1)
\]

So, the factored form of \(-8a^2b + 4ab\) is \(4ab(-2a + 1)\).

Would you like further details or have any questions?

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Here are 8 related questions to expand your understanding:

1. How do you determine the GCF of more complex polynomials?
2. Can you factor \(12x^3y - 8x^2y^2 + 4xy\) using the GCF method?
3. What happens if there is no common factor between the terms?
4. How would you factor a trinomial using the GCF method?
5. How do you apply the GCF method to expressions involving multiple variables?
6. Can you factor a polynomial where one term is negative and the other positive?
7. What is the next step if the factored expression can still be simplified?
8. How does factoring using the GCF differ from factoring by grouping?

**Tip:** Always double-check each term after factoring to ensure the product equals the original expression.

Learn how to factor the expression -8a²b + 4ab using the Greatest Common Factor (GCF) method. Follow a detailed step-by-step solution to understand how to identify the GCF, factor out the common terms, and write the factored form. Suitable for Grades 7-9 students studying polynomial factoring and GCF in algebra.

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