Simplify y/(3y^2-12)*(y^2-4y+4)

$\frac{y}{3 y^{2} - 12} \times (y^{2} - 4 y + 4)$

Simplify the denominator.

Factor $3$ out of $3 y^{2} - 12$ .

Factor $3$ out of $3 y^{2}$ .

$\frac{y}{3 (y^{2}) - 12} \cdot (y^{2} - 4 y + 4)$

Factor $3$ out of $- 12$ .

$\frac{y}{3 y^{2} + 3 \cdot - 4} \cdot (y^{2} - 4 y + 4)$

Factor $3$ out of $3 y^{2} + 3 \cdot - 4$ .

$\frac{y}{3 (y^{2} - 4)} \cdot (y^{2} - 4 y + 4)$

Rewrite $4$ as $2^{2}$ .

$\frac{y}{3 (y^{2} - 2^{2})} \cdot (y^{2} - 4 y + 4)$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 2$ .

$\frac{y}{3 (y + 2) (y - 2)} \cdot (y^{2} - 4 y + 4)$

Multiply $\frac{y}{3 (y + 2) (y - 2)}$ by $y^{2} - 4 y + 4$ .

$\frac{y (y^{2} - 4 y + 4)}{3 (y + 2) (y - 2)}$

Factor using the perfect square rule.

Rewrite $4$ as $2^{2}$ .

$\frac{y (y^{2} - 4 y + 2^{2})}{3 (y + 2) (y - 2)}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 y = 2 \cdot y \cdot 2$

Rewrite the polynomial.

$\frac{y (y^{2} - 2 \cdot y \cdot 2 + 2^{2})}{3 (y + 2) (y - 2)}$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = y$ and $b = 2$ .

$\frac{y {(y - 2)}^{2}}{3 (y + 2) (y - 2)}$

Cancel the common factor of ${(y - 2)}^{2}$ and $y - 2$ .

Factor $y - 2$ out of $y {(y - 2)}^{2}$ .

$\frac{(y - 2) (y (y - 2))}{3 (y + 2) (y - 2)}$

Cancel the common factors.

Factor $y - 2$ out of $3 (y + 2) (y - 2)$ .

$\frac{(y - 2) (y (y - 2))}{(y - 2) (3 (y + 2))}$

Cancel the common factor.

$\frac{(y - 2) (y (y - 2))}{(y - 2) (3 (y + 2))}$

Rewrite the expression.

$\frac{y (y - 2)}{3 (y + 2)}$