(7-k^4)^2

Jasonbradley

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Jun 16, 2024

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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.

1. First: Multiply the first terms of each binomial: 7 * 7 = 49
2. Outer: Multiply the outer terms of the binomials: 7 * (-k^4) = -7k^4
3. Inner: Multiply the inner terms of the binomials: (-k^4) * 7 = -7k^4
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.