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Verified Answer :

Greenleafable

The equation which is supposed to help you is this one:
a^2 - b^2 = (a+b) (a-b)

So, what we need to do here is apply this equation:
k^2 - 9h^2 = 
k * k - (3h)^2 =
(k + 3h) (k-3h)

The correct answer is C.

Answer:  The correct factored form is (C) \((k+3h)(k-3h).\)

Step-by-step explanation:  We are given to write the factored form of the following expression:

\(E=k^2-9h^2.\)

We will be using the following algebraic formula in the factorisation:

\(a^2-b^2=(a+b)(a-b).\)

The factorisation is as follows:

\(E\\\\=k^2-9h^2\\\\=(k)^2-(3h)^2\\\\=(k+3h)(k-3h).\)

Therefore, the factored form is \((k+3h)(k-3h).\)

Thus, (C) is the correct option.

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