Example 6: Solve the following equations by factoring. 1. x^2-4=0 2. 2x^2-18=0

To solve the equations by factoring, we need to factor the quadratic expressions and then set each factor equal to zero to find the solutions.1. We can factor the left side of the equation as a difference of squares: Setting each factor equal to zero gives us the solutions: or or So, the solutions to the equation are and .2. We can factor out a common factor of 2 from the left side of the equation: Now, we can factor the expression inside the parentheses as a difference of squares: Setting each factor equal to zero gives us the solutions: or or So, the solutions to the equation are and .