## Expanding (8x^4 + 1)^2

This expression represents the square of a binomial, which can be expanded using the **FOIL** method or by recognizing the **square of a sum** pattern.

### Using FOIL

**FOIL** stands for **First, Outer, Inner, Last**. This method helps us multiply two binomials by systematically combining all the terms:

**First:**Multiply the first terms of each binomial: (8x^4) * (8x^4) = 64x^8**Outer:**Multiply the outer terms of the binomials: (8x^4) * (1) = 8x^4**Inner:**Multiply the inner terms of the binomials: (1) * (8x^4) = 8x^4**Last:**Multiply the last terms of each binomial: (1) * (1) = 1

Now, add all the results together:

64x^8 + 8x^4 + 8x^4 + 1

Finally, combine the like terms:

**64x^8 + 16x^4 + 1**

### Using the Square of a Sum Pattern

The square of a sum pattern states: (a + b)^2 = a^2 + 2ab + b^2

In our case, a = 8x^4 and b = 1. Applying the pattern:

(8x^4 + 1)^2 = (8x^4)^2 + 2(8x^4)(1) + (1)^2

Simplifying:

**64x^8 + 16x^4 + 1**

Therefore, both methods lead to the same result: **(8x^4 + 1)^2 = 64x^8 + 16x^4 + 1**.