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Methods of Factoring

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A series of free, online Intermediate Algebra Lessons or Algebra II lessons.
Examples, solutions, videos, worksheets, and activities to help Algebra students.

Review of the Methods of Factoring from Algebra I
The first step is to identify the polynomial type in order to decide which factoring methods to use. Next, look for a common term that can be taken out of the expression. A statement with two terms can be factored by a difference of perfect squares or factoring the sum or difference of cubes. For the case with four terms, factoring by grouping is the most effective way. This method is explained in the video on advanced factoring.

The following diagram shows how to factor the sum and difference of cubes. Scroll down the page for more examples and solutions on factoring polynomials.

Sum and Difference of Cubes

Factoring the Sum or Difference of Cubes

When factoring trinomials, we can learn certain patterns of factoring the sum or difference of cubes. When factoring sum of cubes expressions, we will always end up with the binomial (a + b) multiplied by the trinomial (a2 - ab + b2). When factoring the difference of cubes, we will always end up with the binomial (a - b) multiplied by the trinomial (a2 + ab + b2).
Factoring a Sum or Difference of Cubes Factoring Sums and Differences of Cubes
In this video, I use the formulas for factoring sums and differences of cubes. I factor two expressions using the formulas.

Factoring Complicated Expressions: Complex Factoring

When asked to simplify expressions, sometimes we come across complicated expressions that are not easily factored by traditional methods. When factoring complex expressions, one strategy that we can use is substitution. When an expression has complex terms, we can substitute a single variable, factor and then re-substitute the original term for the variable once we have completely factored the expression.
How to factor complicated expressions? Factoring by Substitution

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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