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Factoring or factorising in British English is the process of finding the factors an algebraic term, or writing a term as a multiple of more simple terms. It is the opposite of expanding. A simple example would be:


With the first term being the expanded version and the second factored. A more complex example would be:


Common factoring patterns

Binomials

Binomials tend to appear by themselves as a square:

If raised to higher powers, they continue according to the pattern shown in the Binomial coefficient:

Quadratic formula

The Quadratic formula determines roots, which can be factored from the polynomial.

Difference of squares

One common factoring problem is called a difference of squares. This involves a squared factor minus another squared factor. This type of equation can be written as follows:

An example of this using real numbers would be:

Sum of Squares

Another common factoring problem is the sum of squares. similar to difference of squares, its results are quite different.

An example would be

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