Question

What is the factored form of the expression?

k2 – 9h2
A. (k + 3h)(k + 3h)

B. h2(k + 3)(k – 3)

C. (k + 3h)(k – 3h)

D. (k – 3h2)(k + 3)

Answer 1

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.

Answer 2

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.