1. **State the problem:** Factor out the greatest common factor (GCF) from the polynomial $$a^7 b^6 - a^3 b^2 + a^2 b^5 - a^2 b^2$$. 2. **Identify the GCF:** - For the variable $a$, the powers are 7, 3, 2, and 2. The smallest power is 2. - For the variable $b$, the powers are 6, 2, 5, and 2. The smallest power is 2. Therefore, the GCF is $$a^2 b^2$$. 3. **Factor out the GCF:** $$a^7 b^6 - a^3 b^2 + a^2 b^5 - a^2 b^2 = a^2 b^2 \left(\frac{a^7 b^6}{a^2 b^2} - \frac{a^3 b^2}{a^2 b^2} + \frac{a^2 b^5}{a^2 b^2} - \frac{a^2 b^2}{a^2 b^2}\right)$$ 4. **Simplify inside the parentheses:** $$= a^2 b^2 \left(a^{7-2} b^{6-2} - a^{3-2} b^{2-2} + a^{2-2} b^{5-2} - a^{2-2} b^{2-2}\right)$$ 5. **Calculate the exponents:** $$= a^2 b^2 \left(a^5 b^4 - a^1 b^0 + a^0 b^3 - a^0 b^0\right)$$ 6. **Simplify powers of zero:** $$= a^2 b^2 \left(a^5 b^4 - a + b^3 - 1\right)$$ 7. **Final factored form:** $$\boxed{a^2 b^2 (a^5 b^4 - a + b^3 - 1)}$$