Evaluate (x²-6)²: Solving a Perfect Square of a Binomial

To solve this problem, we'll follow these steps:

• Step 1: Identify a and b in the expression $(x^2 - 6)^2$.
• Step 2: Apply the square of a difference formula.
• Step 3: Simplify the resulting expression.

Now, let's work through each step:
Step 1: The expression is $(x^2 - 6)^2$. Here, $a = x^2$ and $b = 6$.
Step 2: Apply the binomial formula: $(a - b)^2 = a^2 - 2ab + b^2$.
Step 3:
1. Calculate $a^2$:
$a^2 = (x^2)^2 = x^4$.
2. Calculate $2ab$:
$2ab = 2(x^2)(6) = 12x^2$.
3. Calculate $b^2$:
$b^2 = 6^2 = 36$.
4. Substitute these back into the formula:
$(x^2 - 6)^2 = x^4 - 12x^2 + 36$.

Therefore, the expanded expression is $x^4 - 12x^2 + 36$.