## Expanding (7-k^4)^2

The expression (7-k^4)^2 represents the square of the binomial (7-k^4). To expand this, we can use the **FOIL method** or the **square of a binomial formula**.

### Using the FOIL Method

**FOIL** stands for **First, Outer, Inner, Last**. This method helps us multiply two binomials.

**First:**Multiply the first terms of each binomial: 7 * 7 = 49**Outer:**Multiply the outer terms of the binomials: 7 * (-k^4) = -7k^4**Inner:**Multiply the inner terms of the binomials: (-k^4) * 7 = -7k^4**Last:**Multiply the last terms of each binomial: (-k^4) * (-k^4) = k^8

Now, add all the terms together:

49 - 7k^4 - 7k^4 + k^8

Combining like terms, we get the final expanded form:

**k^8 - 14k^4 + 49**

### Using the Square of a Binomial Formula

The square of a binomial formula states: (a - b)^2 = a^2 - 2ab + b^2

In our case, a = 7 and b = k^4

Applying the formula, we get:

(7 - k^4)^2 = 7^2 - 2(7)(k^4) + (k^4)^2

Simplifying the expression:

**k^8 - 14k^4 + 49**

Both methods lead to the same expanded form of (7-k^4)^2: **k^8 - 14k^4 + 49**. This expression is a **quadratic** in terms of k^4.