1. **Stating the problem:** Reduce the expression $$(3a+b)\cdot(2a-4b)-5a^2$$. 2. **Formula and rules:** Use the distributive property to expand the product of two binomials: $$(x+y)(z+w) = xz + xw + yz + yw$$. Remember to combine like terms after expansion. 3. **Expand the expression:** $$(3a+b)(2a-4b) = 3a \cdot 2a + 3a \cdot (-4b) + b \cdot 2a + b \cdot (-4b)$$ $$= 6a^2 - 12ab + 2ab - 4b^2$$ 4. **Simplify the terms inside the parentheses:** $$6a^2 - 12ab + 2ab - 4b^2 = 6a^2 - 10ab - 4b^2$$ 5. **Subtract $5a^2$ from the result:** $$6a^2 - 10ab - 4b^2 - 5a^2$$ 6. **Combine like terms:** $$\cancel{6a^2} - 10ab - 4b^2 - \cancel{5a^2} = (6a^2 - 5a^2) - 10ab - 4b^2 = 1a^2 - 10ab - 4b^2$$ 7. **Final reduced expression:** $$a^2 - 10ab - 4b^2$$