How to Factor the Difference of Two Perfect Squares
If two terms in a binomial are perfect squares separated by subtraction, then you can factor them. To factor the difference of two perfect squares, remember this rule: if subtraction separates two squared terms, then the sum and the difference of the two square roots factor the binomial. For example:
Example 1:
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Find the square roots of the two terms that are perfect squares.
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Write the factorization as the sum and difference of the square roots.
The sum of the roots is 3x + 4 and the difference between the roots is 3x – 4.
Example 2:
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Find the square roots of the two terms that are perfect squares.
Just place the number inside the square root symbol.
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Write the factorization as the sum and difference of the square roots.
