How to Factor Perfect Squares in Algebra

A fundamental skill in algebra is factoring polynomials. The student who masters the special formula To Factor a Perfect Square, as well as the other factoring formulas and skills will be on track to algebra success. It is one of the first algebra skills a student learns. What better way to start a discipline than to get really good at the basics and first steps.

Difficulty: Moderate

Instructions

1. Begin factoring polynomials by looking for any common factors. We call these common monomial factors.

2. Study the equation you are factoring and see if you can apply any of the special formulas. Consider the Difference of Two Squares, Perfect Squares, Difference of Two Cubes or the Sum of Two Cubes formulas.

3. Recognize the perfect square formula. It looks like this: x^2 + 2ax + a^2 = (x + a)^2 and also x^2 – 2ax + a^2 = (x – a)^2.

4. Factor perfect squares by first recognizing the pattern: x^2 + 4x + 4, 16x^2 – 8x + 1, 9x^2 +18x + 9. Translate the polynomial forms respectively: x^2 + Bx + C and Ax^2 + Bx + C.

5. Notice that the first terms of A in these perfect squares is the square x^2, 4^2 and 3^2 respectively. Now look at the C terms above: 2^2, 1^2 and 3^2, also squares. See how the B term in each is twice the product of the A and C terms.

6. Finish up this lesson by factoring the perfect squares in step 4. The first is x^2 + 4x + 4 = (x + 2)^2. The next one is 16x^2 – 8x + 1 = (4x – 1)^2. Finally we have 9x^2 + 18x + 9 = (3x + 3)^2.

7. Examine these steps for factoring perfect squares closely to master your first steps in algebra.