Expand. (Simplify your answer completely.)

(*x*2 − 4)2

To simplify the expression \((x^2 - 4)^2\), follow these steps:

### Step 1: Recognize the binomial squared.
We are squaring the binomial \(x^2 - 4\). Use the formula for squaring a binomial:
\[
(a - b)^2 = a^2 - 2ab + b^2
\]
Here, \(a = x^2\) and \(b = 4\).

### Step 2: Apply the formula.
\[
(x^2 - 4)^2 = (x^2)^2 - 2(x^2)(4) + 4^2
\]

### Step 3: Simplify each term.
\[
(x^2)^2 = x^4
\]
\[
-2(x^2)(4) = -8x^2
\]
\[
4^2 = 16
\]

### Step 4: Combine the terms.
\[
x^4 - 8x^2 + 16
\]

Thus, the fully simplified expression is:
\[
x^4 - 8x^2 + 16
\]

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Would you like more details or have any questions?

### Related Questions:
1. How would you simplify \((x + 3)^2\)?
2. Can you expand \((2x^2 - 5)^2\) using a similar method?
3. What is the expanded form of \((x^3 - 2)^2\)?
4. How do you factor the expression \(x^4 - 8x^2 + 16\) back into binomials?
5. What is the general formula for expanding \((a - b)^n\)?

**Tip:** Always apply the distributive property or use known formulas like the binomial expansion when simplifying expressions.

Expand. (Simplify your answer completely.) (*x*2 − 4)^2

This guide walks through the steps to simplify and expand the algebraic expression (x^2 − 4)^2 using binomial expansion and polynomial simplification techniques. Ideal for students in Grades 9-11.

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