Most students learn to factor polynomials by finding the greatest common factor (GCF), factoring trinomials, or using the difference of squares. But what happens when you’re asked to factor an expression containing perfect cubes? Unlike the difference of squares, both the sum and difference of cubes can be factored using special patterns.
In this video, you’ll learn how to factor the sum and difference of cubes, two important factoring patterns that allow you to rewrite cubic expressions as products of a binomial and a trinomial. Rather than guessing at possible factors, you’ll learn how to recognize perfect cubes, identify the correct factoring pattern, and use the signs to factor expressions accurately.
We’ll walk through the process step by step, showing how to identify perfect cubes, find their cube roots, construct the binomial and trinomial factors, and use the SOAP method (Same, Opposite, Always Positive) to remember the correct signs.
In this lesson you’ll learn:
• What the sum and difference of cubes are and how to recognize them
• How to identify perfect cubes involving numbers and variables
• How to find the cube root of each term in a polynomial
• The factoring patterns for the sum and difference of cubes
• How to use SOAP (Same, Opposite, Always Positive) to remember the signs
• How to find the middle term by multiplying the cube roots
• Why the last term of the trinomial is always positive
• Common mistakes students make when factoring the sum and difference of cubes
By the end of this lesson, you’ll understand how the sum and difference of cubes factoring patterns work and how to use them to factor cubic expressions efficiently and accurately. You’ll also recognize how these patterns connect to polynomial multiplication and why understanding the structure of an expression makes factoring easier.
Whether you’re taking Algebra 1, Algebra 2, Honors Algebra 2, Precalculus, or preparing for the ACT or SAT, recognizing special factoring patterns is an important skill that strengthens your ability to simplify polynomial expressions and solve equations.
