The expression you have uploaded is:

$x^2 - x - (a + 1)(a + 2)$

Let's break this down and simplify it step by step:

Step 1: Expand the product $(a + 1)(a + 2)$

Using the distributive property:

$(a + 1)(a + 2) = a(a + 2) + 1(a + 2)$ $= a^2 + 2a + a + 2$ $= a^2 + 3a + 2$

Step 2: Substitute this result back into the original expression

Now the expression becomes:

$x^2 - x - (a^2 + 3a + 2)$

Step 3: Simplify the expression

Distribute the negative sign:

$x^2 - x - a^2 - 3a - 2$

This is the simplified form of the given expression:

$x^2 - x - a^2 - 3a - 2$

Would you like further details on any of the steps?

Here are five related questions you might consider:

1. How do you factor quadratic expressions like $(a+1)(a+2)$?
2. What happens when you need to solve $x^2 - x - a^2 - 3a - 2 = 0$ for $x$?
3. How can you use the quadratic formula for equations in the form $x^2 + bx + c = 0$?
4. What is the significance of the distributive property in expanding expressions?
5. How do you combine like terms in an algebraic expression?

Tip: When simplifying algebraic expressions, always expand products first and then combine like terms carefully!