Question

identify the excluded values of this product. then rewrite the product in simplest form.\\(\frac{6y^2 + 18y - 60}{3y^2 - 12y} cdot \frac{y^2 - 18}{y^2 + 2y - 8}\\)\
type the correct answer in the box. do not type the excluded values.

Explanation:

Step1: Factor all polynomials

1. Numerator 1: $6y^2 + 18y - 60 = 6(y^2 + 3y - 10) = 6(y+5)(y-2)$
2. Denominator 1: $3y^2 - 12y = 3y(y-4)$
3. Numerator 2: $y^2 - 16 = (y+4)(y-4)$
4. Denominator 2: $y^2 + 2y - 8 = (y+4)(y-2)$

Substitute back into the product:
$$\frac{6(y+5)(y-2)}{3y(y-4)} \cdot \frac{(y+4)(y-4)}{(y+4)(y-2)}$$

Step2: Cancel common factors

Cancel $3$, $(y-2)$, $(y-4)$, $(y+4)$ from numerator and denominator:
$$\frac{6 \div 3 \cdot (y+5)}{y} = \frac{2(y+5)}{y}$$

Step3: Simplify the expression

Expand the remaining numerator:
$$\frac{2y + 10}{y}$$

Answer:

$\frac{2y+10}{y}$ or $2 + \frac{10}{y}$