1. We are asked to expand the expression $$(x+4)(x-5)(x+3)$$. 2. First, expand two of the factors, for example, $(x+4)(x-5)$: $$ (x+4)(x-5) = x \cdot x + x \cdot (-5) + 4 \cdot x + 4 \cdot (-5) = x^2 - 5x + 4x - 20 = x^2 - x - 20 $$ 3. Now multiply this result by the remaining factor $(x+3)$: $$ (x^2 - x - 20)(x + 3) = (x^2 - x - 20) \cdot x + (x^2 - x - 20) \cdot 3 $$ 4. Distribute: $$ = x^3 - x^2 - 20x + 3x^2 - 3x - 60 $$ 5. Combine like terms: $$ x^3 + (- x^2 + 3x^2) + (-20x - 3x) - 60 = x^3 + 2x^2 - 23x - 60 $$ 6. Final expanded form is: $$ x^3 + 2x^2 - 23x - 60 $$