Factoring is all about breaking a polynomial into products of smaller, more manageable, parts.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
The first, and arguably the most important rule of factoring is to look for and pull out the Greatest Common Factor, but this isn’t the only tool in our tool-belt.
An incredibly useful skill is knowing how to factor binomials; factoring the difference of two squares!
So were do we begin?
First, we pull out the GCF, if possible, then we look to see if the polynomial is a binomial
A binomial, remember, is a polynomial with only two terms.
Second, we check to see if our binomial is “special.”
What do I mean by “special”?
We need to determine if the first term is a perfect square and the last term is a perfect square.
Recall, that a perfect square is the product of a number multiplied by itself.
Finally, we must verify that a negative sign separates both of these terms. If so, this means it is factorable, and we can use the Difference of Squares Formula!
Factoring the Difference of Squares
As you will quickly see, after countless examples, that factoring these types of binomials are super easy because they follow a very easy to use formula, and we can always check our work by FOILing.
But, as Purple Math warns, we must never forget that the difference of squares formula is only used when there is a subtraction sign (difference) between two perfect squares. If you see addition (sum) between the two terms, then the answer is prime and cannot be factored further.
Factoring Difference of Squares (How-To) – Video
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