To add the given expressions, we need to carefully combine like terms. However, it seems there are some inconsistencies in the way the expressions are written. I'll assume the following interpretation for the three given expressions:

1. \(-5x^2 + 6xy - 18y^2\)
2. \(2xy\)
3. \(10y^2 - x^2 + 1\)

Let's add these expressions step-by-step.

### Step 1: Write all expressions in a standard format

1. \(-5x^2 + 6xy - 18y^2\)
2. \(2xy\)
3. \(10y^2 - x^2 + 1\)

### Step 2: Combine like terms

- **Combine \(x^2\) terms:**
  \[
  -5x^2 - x^2 = -6x^2
  \]

- **Combine \(xy\) terms:**
  \[
  6xy + 2xy = 8xy
  \]

- **Combine \(y^2\) terms:**
  \[
  -18y^2 + 10y^2 = -8y^2
  \]

- **Combine constant terms:**
  \[
  1
  \]

### Step 3: Sum the combined terms

Combining all the results:

\[
-6x^2 + 8xy - 8y^2 + 1
\]

### Final result

\[
-6x^2 + 8xy - 8y^2 + 1
\]

Do you want details or have any questions?

Here are 5 more questions you might want to ask:

1. How do I simplify expressions with multiple variables?
2. Can you explain how to combine like terms in algebra?
3. What are the steps to solve a quadratic equation?
4. How do I factor polynomials with two variables?
5. Can you demonstrate how to complete the square for a quadratic equation?

**Tip:** When combining like terms, make sure to align the terms correctly by their variable and exponent to avoid any mistakes.

Learn how to add the expressions -5x^2 + 6xy - 18y^2, 2xy = 7x^2 = y^2 and 10y^2 - x^2 + 1 with a step-by-step solution. This problem involves combining like terms in algebraic expressions and is suitable for Grades 7-9.

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