Solve by Factoring x^2-16=0

Problem

x^2−16=0

Solution

1. Identify the expression on the left side as a difference of squares, which follows the pattern a^2−b^2=(a−b)*(a+b)

2. Rewrite the constant 16 as 4^2 to clearly see the squares.

3. Factor the expression x^2−4^2 into (x−4)*(x+4)

4. Apply the zero product property by setting each factor equal to zero.

5. Solve the resulting linear equations x−4=0 and x+4=0 to find the values of x

x^2−16=0

(x−4)*(x+4)=0

x−4=0⇒x=4

x+4=0⇒x=−4

Final Answer

x=4,−4

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