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The difference of squares formula is one of the primary algebraic formulas used to expand a term in the form of . Basically, it is an algebraic form of an expression used to equate the differences between two square values. The formula helps make a complex equation into a simple one.
Any polynomial that can be written as can be factored as the difference of a square.
The reason is that when you use FOIL to expand the right side, the ab terms cancel out as follows:
Example 1
Take the equation
Using the difference of squares formula,
where
To calculate the left hand side (LHS),
To calculate the right hand side (RHS),
This demonstrates that the formula works correctly.
Example 2
What is the value of ?
The formula for the difference of squares is:
Therefore, from the given expression,
We can double check that this is correct by performing the calculations on the original problem.
And we've simplified the problem correctly again.
Frequently in algebra problems, the point of the difference of squares identity is to factor the statement, not to find the value of an expression as in the previous example. This can be done with variables, which you will usually find in algebraic problems.
Example 3
Factor, if possible.
This is a difference of squares where and
Example 4
Factor, if possible.
This is a difference of squares where and .
We can be confident that these examples are factored correctly because of the first example where we solved the entire problem, making sure that the formula works properly.
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