Here's a factorization problem for you. We need to factor the expression x squared minus 4. This is a classic example of a difference of squares pattern.
The first step is to recognize that x squared minus 4 follows the difference of squares pattern. The general formula is a squared minus b squared equals a minus b times a plus b. In our case, a equals x and b equals 2.
Now we apply the difference of squares formula. We have x squared minus 4. First, we identify that a equals x and b equals 2, since 4 equals 2 squared. Then we substitute these values into the formula to get x minus 2 times x plus 2.
Let's verify our answer by expanding x minus 2 times x plus 2 using the FOIL method. First times first gives x squared. Outer times gives 2x. Inner times gives negative 2x. Last times gives negative 4. Combining these terms, we get x squared plus 2x minus 2x minus 4, which simplifies to x squared minus 4. This matches our original expression, confirming our factorization is correct.
To summarize our factorization: We successfully factored x squared minus 4 by recognizing it as a difference of squares pattern. We identified x as a and 2 as b, then applied the formula to get x minus 2 times x plus 2. We verified this answer by expanding it back to the original expression.