https://file.aiquickdraw.com/mathbot/file/1729583756058o56gdkrb.jpg

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!

Simplify the expression: x^2 - x - (a + 1)(a + 2)

Learn how to simplify the algebraic expression x^2 - x - (a + 1)(a + 2) by expanding and combining like terms. This problem covers key algebraic concepts, including the distributive property and expression simplification. Suitable for students in Grades 8-10.

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