Question

Ginger was asked to solve 16x2−1 by using the difference of two squares pattern. What is/are the correct solution(s)?(1 point) Responses x=14 x is equal to 1 fourth x=116 x is equal to 1 over 16 x=−14 , x=14 x is equal to negative 1 fourth, x is equal to 1 fourth There is no solution for x because the difference of squares pattern does not apply.

Answer 1

Pick kne

Answer 2

To solve the expression \(16x^2 - 1\) using the difference of squares pattern, we recognize that it can be factored as follows:

\[
16x^2 - 1 = (4x)^2 - (1)^2
\]

This can be factored into:

\[
(4x - 1)(4x + 1) = 0
\]

Next, we set each factor to zero to find the solutions for \(x\):

1. \(4x - 1 = 0\)
- Solving for \(x\):
\[
4x = 1 \quad \Rightarrow \quad x = \frac{1}{4}
\]

2. \(4x + 1 = 0\)
- Solving for \(x\):
\[
4x = -1 \quad \Rightarrow \quad x = -\frac{1}{4}
\]

Thus, the solutions are:

\[
x = \frac{1}{4} \quad \text{and} \quad x = -\frac{1}{4}
\]

Now, looking at the responses you provided, the correct solution(s) would be:

- \(x = -\frac{1}{4}, x = \frac{1}{4}\)

So, you would select the response that includes both of these values.

Answer 3

The correct response to select is:

**"x = -1/4, x = 1/4"**

This encompasses both solutions found by factoring the expression \(16x^2 - 1\).