Expand and Simplify: 6x(-2x+3y)+12x² | Algebraic Expression

To solve this problem, we'll follow these steps:

• Step 1: Apply the distributive property to expand the expression.
• Step 2: Simplify the expression by combining like terms.

Now, let's work through each step:

Step 1: Apply the distributive property to $6x(-2x + 3y)$.
This gives us:
$6x \cdot (-2x) + 6x \cdot (3y) = -12x^2 + 18xy$.

Step 2: Add this result to $12x^2$:
$-12x^2 + 18xy + 12x^2$.

Combine like terms:
$-12x^2 + 12x^2$ cancels out, leaving $18xy$.

Therefore, the simplified form of the expression is $18xy$.