1. **State the problem:** Simplify the expression $$6a^3b^5 - 14a^2b^4 + 10a^3b$$. 2. **Identify common factors:** Look for the greatest common factor (GCF) in all terms. - For coefficients: GCF of 6, 14, and 10 is 2. - For variable $a$: minimum power is $a^2$ (since powers are 3, 2, and 3). - For variable $b$: minimum power is $b^1$ (powers are 5, 4, and 1). 3. **Factor out the GCF:** $$\text{GCF} = 2a^2b$$ 4. **Rewrite each term by factoring out the GCF:** $$6a^3b^5 = 2a^2b \times 3ab^4$$ $$-14a^2b^4 = 2a^2b \times (-7b^3)$$ $$10a^3b = 2a^2b \times 5a$$ 5. **Express the original expression as:** $$6a^3b^5 - 14a^2b^4 + 10a^3b = 2a^2b(3ab^4 - 7b^3 + 5a)$$ 6. **Final answer:** $$\boxed{2a^2b(3ab^4 - 7b^3 + 5a)}$$ This is the simplified factored form of the expression.