We are given the expression:

$\left(a^2 + b^2\right)\left(a + b\right)\left(a - b\right)$

To simplify this, we can use known algebraic identities.

First, recognize that the product $(a + b)(a - b)$ is the difference of squares identity:

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

Substituting this into the expression, we get:

$\left(a^2 + b^2\right)\left(a^2 - b^2\right)$

Now, expand this product using the distributive property:

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

Distribute the terms:

$= a^4 - a^2b^2 + b^2a^2 - b^4$

Notice that $-a^2b^2$ and $b^2a^2$ cancel out:

$a^4 - b^4$

Thus, the simplified expression is:

$a^4 - b^4$

Final answer:

$a^4 - b^4$

Would you like more details on the steps involved or have any questions?

Here are five related questions:

1. How does the difference of squares identity work?
2. What happens if $a = b$ in this expression?
3. Can this expression be factored further if $a^4 - b^4$ was treated as a difference of squares?
4. How does this process change if there were higher powers of $a$ and $b$?
5. How would the result differ if the original expression had $a^2 - b^2$ instead of $a^2 + b^2$?

Tip: Always look for common algebraic identities like the difference of squares to simplify complex expressions.