We are asked to factor the expression $x^2 - 49$ using the difference of two squares formula.

AlgebraFactorizationDifference of SquaresAlgebraic Expressions
2025/3/26

1. Problem Description

We are asked to factor the expression x249x^2 - 49 using the difference of two squares formula.

2. Solution Steps

The difference of two squares formula is given by:
a2b2=(ab)(a+b)a^2 - b^2 = (a - b)(a + b)
In the given expression, x249x^2 - 49, we can rewrite it as x272x^2 - 7^2.
Here, a=xa = x and b=7b = 7. Applying the difference of two squares formula:
x272=(x7)(x+7)x^2 - 7^2 = (x - 7)(x + 7)

3. Final Answer

(x7)(x+7)(x-7)(x+7)