Question

Somebody please help!
Simplify the following expression:
(x+5)(3x-1)(3x-2)

Answer 1

9x^3+36x^2-43x+10

Explanation:

(x+5)(3x-1)(3x-2)

First solve (x+5)(3x-1):

3x^2-x+15x-5

3x^2+14x-5

Then use that to multiply with (3x-2)

(3x^2+14x-5)(3x-2)

9x^3-6x^2+42x^2-28x-15x+10

9x^3+36x^2-43x+10

Answer:

9x^3+36x^2-43x+10

Answer 2

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.