How Do You Factor the Difference of Two Squares?


Quick Answer

To factor the difference of two squares, break down the squares, and then factor them out to get the positive and negative solutions. The proper solution includes the sum and the difference of the two square roots, multiplied together.

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Full Answer

  1. Find the squares and square roots involved

    Consider the example problem x^2 - 9. Break down x^2 and 9 into their square roots, which are x and either 3 or (-3). Remember that this only works for variables and constants that break down into perfect square roots, so numbers such as 8 and variable expressions such as 2x^5 do not factor this way.

  2. Write the factors in proper form

    Remember that for any expression a^2 - b^2, the proper way to present the factoring is as follows: (a + b) (a - b). Look at the example problem from Step 1, and write the factors in the proper way: (x + 3) (x - 3).

  3. Remember to factor constants with variables

    Consider the example problem 9z^2 - 16x^6. Break these two perfect squares down correctly by finding the square roots of both their constants and variables. Write the correct answer to this example problem in this format: (3z + 4x^3) (3z - 4x^3).

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