1. The problem asks which expression can be factored to $$3xy(2x + 1)(x - 4)$$. 2. To check, we expand the factored form using the distributive property: $$3xy(2x + 1)(x - 4) = 3xy \times [(2x)(x) + (2x)(-4) + (1)(x) + (1)(-4)]$$ 3. Simplify inside the brackets: $$= 3xy \times (2x^2 - 8x + x - 4) = 3xy \times (2x^2 - 7x - 4)$$ 4. Now distribute $$3xy$$: $$= 3xy \times 2x^2 - 3xy \times 7x - 3xy \times 4 = 6x^3y - 21x^2y - 12xy$$ 5. Compare this result to the given options: - a) $$9x^2y - 9xy$$ - b) $$2x^2 - 7x - 4$$ - c) $$6x^3y - 21x^2y - 12xy$$ - d) $$18x^4y^2 - 63x^3y^2 - 36x^2y^2$$ 6. The expanded expression matches option c). Final answer: c) $$6x^3y - 21x^2y - 12xy$$