Answer:
To simplify the expression (x+5)(3x-1)(3x-2), we can use the distributive property of multiplication and combine like terms:
(x+5)(3x-1)(3x-2)
= (x(3x-1)+5(3x-1))(3x-2) [distributive property of multiplication]
= (3x^2-x+15x-5)(3x-2) [distributive property of multiplication again]
= (3x^2+14x-5)(3x-2) [combine like terms]
To multiply the two factors, we can use the FOIL method:
(3x^2+14x-5)(3x-2)
= 3x^2(3x) + 14x(3x) - 5(3x) - 2(3x^2) - 2(14x) + 2(5) [FOIL method]
= 9x^3 + 42x^2 - 15x - 6x^2 - 28x + 10 [combine like terms]
= 9x^3 + 36x^2 - 43x + 10 [combine like terms]
Therefore, (x+5)(3x-1)(3x-2) simplifies to 9x^3 + 36x^2 - 43x + 10.