## Simplifying the Expression: (x^2 + 8)^2 - 36x^2

This expression looks complicated, but we can simplify it using basic algebraic manipulations. Here's how we can approach it:

### Expanding the Square

First, let's expand the squared term:

**(x^2 + 8)^2 = (x^2 + 8)(x^2 + 8)**

Using the FOIL method (First, Outer, Inner, Last), we get:

**(x^2 + 8)^2 = x^4 + 8x^2 + 8x^2 + 64**

Simplifying:

**(x^2 + 8)^2 = x^4 + 16x^2 + 64**

### Combining Terms

Now, let's substitute this back into the original expression:

**(x^2 + 8)^2 - 36x^2 = (x^4 + 16x^2 + 64) - 36x^2**

Finally, combine the x^2 terms:

**(x^4 + 16x^2 + 64) - 36x^2 = ** **x^4 - 20x^2 + 64**

### Conclusion

Therefore, the simplified form of the expression (x^2 + 8)^2 - 36x^2 is **x^4 - 20x^2 + 64**.