Gabriel was asked to solve x2−36=0 by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point)

Question

Responses

x=6, x=−6
x equals 6 , x equals negative 6

x=−6
x equals negative 6

x=18, x=−18
x equals 18 , x equals negative 18

x=6

Answer 1

To solve the equation \( x^2 - 36 = 0 \) by factoring using the difference of squares pattern, we can recognize that \( x^2 - 36 \) can be written as:

\[ x^2 - 6^2 = 0 \]

This can be factored using the difference of squares formula, which states that \( a^2 - b^2 = (a - b)(a + b) \). Applying this to our equation:

\[ (x - 6)(x + 6) = 0 \]

Now, we set each factor equal to zero:

1. \( x - 6 = 0 \) → \( x = 6 \)
2. \( x + 6 = 0 \) → \( x = -6 \)

Therefore, the solutions are:

\[ x = 6 \quad \text{and} \quad x = -6 \]

The correct answers from your responses are:

x=6, x=−6 and x equals 6 , x equals negative 6.