The expression \((b^4 - 2)^2\) is a square of a binomial. To expand it, we apply the binomial expansion formula:

\[
(a - b)^2 = a^2 - 2ab + b^2
\]

Here, \(a = b^4\) and \(b = 2\). Applying the formula:

\[
(b^4 - 2)^2 = (b^4)^2 - 2(b^4)(2) + 2^2
\]

Now, simplify each term:

1. \((b^4)^2 = b^8\)
2. \( - 2(b^4)(2) = -4b^4\)
3. \( 2^2 = 4 \)

So the expanded form is:

\[
b^8 - 4b^4 + 4
\]

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. How do you factor a binomial squared expression?
2. What are other common binomial identities?
3. How can you apply this expansion to solve for specific values of \(b\)?
4. How does this expression behave when \(b\) is a complex number?
5. What is the geometric significance of squaring a binomial?

**Tip:** Always check if an expression can be factored before expanding it—it might save you some time!

Learn how to expand the expression (b^4 - 2)² using the binomial expansion formula. This problem covers key algebraic concepts such as exponents and the binomial theorem. Suitable for students in Grades 9-11 looking to strengthen their understanding of algebra and polynomial expansion.

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