Final answer:
To simplify the given product, factor each part of the expression and cancel out common factors. The simplest form is 2(y+5)/y, and the excluded values are y = 0, y = 4, and y = 2, where the original expression's denominators are zero.
Step-by-step explanation:
To identify the excluded values of the given product and rewrite it in simplest form, we first factor where possible to find the values that make any denominator zero, as these are the excluded values. The expression provided is (6y²+18y-60)/(3y²-12y) · (y²-16)/(y²+2y-8). Factoring each part:
The first numerator, 6y²+18y-60, factors to 6(y+5)(y-2).
The first denominator, 3y²-12y, factors to 3y(y-4).
The second numerator, y²-16, is a difference of squares and factors to (y+4)(y-4).
The second denominator, y²+2y-8, factors to (y+4)(y-2).
Now the product is: [6(y+5)(y-2)]/[3y(y-4)] · [(y+4)(y-4)]/[(y+4)(y-2)]. We can cancel out the common factors:
(y-4) in the second numerator and first denominator.
(y+4) in the second numerator and second denominator.
(y-2) in the first numerator and second denominator.
After canceling, we are left with 2(y+5)/y. The excluded values are y = 0, y = 4, and y = 2 because at these values, the original denominators would be zero.