Simplify 1/2y^2(6x+2y+12x-2y)

$\frac{1}{2} y^{2} (6 x + 2 y + 12 x - 2 y)$

Step 1

Combine the opposite terms in $6 x + 2 y + 12 x - 2 y$ .

Subtract $2 y$ from $2 y$ .

$\frac{1}{2} \cdot (y^{2} (6 x + 12 x + 0))$

Add $6 x + 12 x$ and $0$ .

$\frac{1}{2} \cdot (y^{2} (6 x + 12 x))$

Step 2

Add $6 x$ and $12 x$ .

$\frac{1}{2} \cdot (y^{2} (18 x))$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $y^{2} (18 x)$ .

$\frac{1}{2} \cdot (2 (y^{2} (9 x)))$

Cancel the common factor.

$\frac{1}{2} \cdot (2 (y^{2} (9 x)))$

Rewrite the expression.

$y^{2} (9 x)$

Step 4

Rewrite using the commutative property of multiplication.

$9 y^{2} x$