Question

Solve 4x^2−64=0
using the difference of squares pattern.(1 point)
Responses

x=−4
x equals negative 4

x=8
, x=−8
x equals 8 , x equals negative 8

x=4
x equals 4

x=4
, x=−4

Answer 1

To solve the equation \( 4x^2 - 64 = 0 \) using the difference of squares pattern, we can first rewrite it in a form that highlights the difference of squares.

1. Start with the equation:
\[
4x^2 - 64 = 0
\]

2. Factor out the common term:
\[
4(x^2 - 16) = 0
\]

3. Now, we can use the difference of squares. Recall that \( a^2 - b^2 = (a - b)(a + b) \). Here, \( x^2 - 16 \) can be expressed as:
\[
x^2 - 4^2
\]

4. Apply the difference of squares:
\[
4(x - 4)(x + 4) = 0
\]

5. Set each factor equal to zero:
\[
x - 4 = 0 \quad \text{or} \quad x + 4 = 0
\]

6. Solve for \( x \):
\[
x = 4 \quad \text{or} \quad x = -4
\]

Thus, the solutions to the equation \( 4x^2 - 64 = 0 \) are:
\[
x = 4, \quad x = -4
\]

The responses matching this solution are:
- \( x = 4, \; x = -4 \)
- \( x \text{ equals } 4 \; \text{and} \; x \text{ equals } negative 4 \)

So the correct options would be:
\( x = 4, \; x = -4 \)