Let's simplify the given expression \((a + b)(a + b)(a - b)\).

### Step 1: First, simplify \((a + b)(a + b)\)
This is the square of a binomial, which follows the identity:
\[
(a + b)^2 = a^2 + 2ab + b^2
\]
So, we have:
\[
(a + b)(a + b) = a^2 + 2ab + b^2
\]

### Step 2: Multiply \((a^2 + 2ab + b^2)\) by \((a - b)\)
Now, distribute \((a^2 + 2ab + b^2)\) with \((a - b)\):
\[
(a^2 + 2ab + b^2)(a - b)
\]

Using distributive property:
\[
(a^2 + 2ab + b^2)(a) - (a^2 + 2ab + b^2)(b)
\]

Now, expand each term:

1. \((a^2 + 2ab + b^2)(a)\):
\[
a^3 + 2a^2b + ab^2
\]

2. \((a^2 + 2ab + b^2)(b)\):
\[
a^2b + 2ab^2 + b^3
\]

Now subtract the two results:
\[
(a^3 + 2a^2b + ab^2) - (a^2b + 2ab^2 + b^3)
\]

Simplifying:
\[
a^3 + 2a^2b + ab^2 - a^2b - 2ab^2 - b^3
\]

Combine like terms:
\[
a^3 + (2a^2b - a^2b) + (ab^2 - 2ab^2) - b^3
\]
\[
= a^3 + a^2b - ab^2 - b^3
\]

### Final result:
The simplified form of \((a + b)(a + b)(a - b)\) is:
\[
a^3 + a^2b - ab^2 - b^3
\]

Would you like further details on any of the steps?

### Related Questions:
1. How do you apply the distributive property for more complex expressions?
2. Can this approach be generalized to higher powers of binomials?
3. How does factoring work for cubes, and how does it relate to this problem?
4. What is the difference between expanding and factoring polynomials?
5. How can you apply the difference of squares identity to simplify similar problems?

**Tip:** Always look for common identities like the difference of squares and perfect square trinomials to simplify binomial expressions quickly.

Explore how to simplify the expression (a+b)(a+b)(a-b) step-by-step using algebraic techniques like the distributive property and the difference of squares identity. This guide covers essential algebra concepts suitable for students in Grades 9-11.

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