Using the Zero-Product Property to Solve a Quadratic Equation Written as the Difference of Squares

Solve the difference of squares equation using the zero-product property: $x^{2} - 9 = 0.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Recognizing that the equation represents the difference of squares, we can write the two factors by taking the square root of each term, using a minus sign as the operator in one factor and a plus sign as the operator in the other. Solve using the zero-factor property.

$\begin{matrix} x^{2} - 9 & = & 0 \\ (x - 3) (x + 3) & = & 0 \\ (x - 3) & = & 0 \\ x & = & 3 \\ (x + 3) & = & 0 \\ x & = & −3 \end{matrix}$
The solutions are $3$ and $−3.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve by factoring: $x^{2} - 25 = 0.$

How did it go?