Solve 16x2−64=0using the difference of squares pattern.(1 point)Responsesx=−2x is equal to negative 2x=−2and x=2x is equal to negative 2 and x is equal to 2x=2x is equal to 2x=−8and x=8

Answer 1

To solve the equation \(16x^2 - 64 = 0\) using the difference of squares pattern, we can first rewrite the equation in a suitable form.

1. Start with the original equation: \[ 16x^2 - 64 = 0 \]

2. We can factor out a common factor, which in this case is 16: \[ 16(x^2 - 4) = 0 \]

3. Next, we can set the expression inside the parenthesis equal to zero: \[ x^2 - 4 = 0 \]

4. Now we recognize that this is a difference of squares, which can be factored further: \[ (x - 2)(x + 2) = 0 \]

5. Setting each factor equal to zero gives us the solutions: \[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \] \[ x + 2 = 0 \quad \Rightarrow \quad x = -2 \]

Thus, the solutions are: \[ x = -2 \quad \text{and} \quad x = 2 \]

So the correct response is: x is equal to negative 2 and x is equal to 2.