This expression is:

$2a \cdot (a - b) + (a + b)^2 - b^2$

Let's simplify this step-by-step.

Step 1: Expand $2a \cdot (a - b)$

$2a \cdot (a - b) = 2a^2 - 2ab$

Step 2: Expand $(a + b)^2$

$(a + b)^2 = a^2 + 2ab + b^2$

Step 3: Rewrite the entire expression

Substitute the expansions into the original expression: $(2a^2 - 2ab) + (a^2 + 2ab + b^2) - b^2$

Step 4: Combine like terms

Group all terms together: $2a^2 - 2ab + a^2 + 2ab + b^2 - b^2$

Simplify:

• $2ab - 2ab = 0$
• $b^2 - b^2 = 0$
• $2a^2 + a^2 = 3a^2$

Final Simplified Expression:

$3a^2$

Would you like additional explanation or further analysis?

Here are five related questions to expand on this concept:

1. How do you simplify expressions involving more variables?
2. Can you show how to factorize quadratic expressions like $3a^2$?
3. What happens when we add or subtract more powers of $a$ and $b$?
4. Can you explain the general process of expanding a polynomial?
5. How can simplifications like this apply to solving equations?

Tip: Always group like terms carefully to simplify your expressions efficiently.