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:

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Example 1:

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  1. Find the square roots of the two terms that are perfect squares.

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  2. 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.

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Example 2:

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  1. Find the square roots of the two terms that are perfect squares.

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    Just place the number inside the square root symbol.

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  2. Write the factorization as the sum and difference of the square roots.

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