Explanation:
First, let's multiply the factors using the distributive property.
(y = (6 - x)(5 - x)(x + 1))
= (6 - x)(5 - x)x + (6 - x)(5 - x)(1)
Next, we can simplify each term separately.
(6 - x)(5 - x)x = (30 - 6x - 5x + x^2)x
= 30x - 6x^2 - 5x^2 + x^3
(6 - x)(5 - x)(1) = (30 - 6x - 5x + x^2)(1)
= 30 - 6x - 5x + x^2
Now, we can combine the simplified terms.
y = (30x - 6x^2 - 5x^2 + x^3) + (30 - 6x - 5x + x^2)
= x^3 - 11x^2 + 19x + 30
Therefore, the cubic function y = (6 - x)(5 - x)(x + 1) in standard form is y = x^3 - 11x^2 + 19x + 30.