How Do You Factor a Perfect Square Trinomial?

Factoring a perfect square trinomial involves recognizing that it can be expressed as the square of a binomial. A perfect square trinomial has the form a² + 2ab + b² or a² – 2ab + b².

To factor it, follow these steps:

1. Identify the coefficients:
• a² is the square of the first term, so find the square root of it, which gives you a.
• b² is the square of the last term, so find the square root of it, which gives you b.
2. Check the middle term:
• For the trinomial to be a perfect square, the middle term (2ab) should equal 2 * a * b.
3. Write it in binomial form:
• If the trinomial is of the form a² + 2ab + b², it factors to (a + b)².
• If it is of the form a² – 2ab + b², it factors to (a – b)².

For example, consider the trinomial x² + 6x + 9. Here, a = x and b = 3, and since 6x = 2 * x * 3, it confirms that it’s a perfect square trinomial. Thus, it factors to (x + 3)².