Simplify the Expression: 6x×3y + 4x² - 10y² + 2x(-ay)

To simplify the expression $6x \times 3y + 4x \times x - 5y \times 2y + 2x(-ay)$, we follow these steps:

• **Step 1:** Calculate each product separately.

• **Step 2:** Combine like terms.

• **Step 3:** Present the simplified expression.

**Detailed Steps:**

**Step 1:** Calculate each product.
- The term $6x \times 3y$ simplifies to $18xy$.
- The term $4x \times x$ is $4x^2$.
- The term $5y \times 2y$ simplifies to $10y^2$.
- The term $2x(-ay)$ becomes $-2axy$.

**Step 2:** Combine like terms:
The terms $18xy$ and $-2axy$ have like variables but do not combine due to the presence of $a$. Thus, focus on properly simplifying other like terms first.

**Step 3:** Simplify the expression:
- Combine $18xy$ and $-2axy$, these remain as separate terms due to different coefficients (one involving $a$).
Thus, the simplified expression becomes:
- The expression after removing, subtracting, or not combining the products effectively boils down to: $4x^2 - 10y^2$.

Therefore, the solution to the problem is $4x^2 - 10y^2$