How to Factor the Difference of Two Perfect Squares

Ever been asked to factor an algebraic expression where both parts of the intended problem have perfect square root-able answers. Well, to solve these types of questions, is fairly easy. This article can tell you how to factor these things.

Steps

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    Determine the problem that needs to be answered. Read the directions along with the intended problem. Write down your problem on a sheet of paper.
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    Make sure all numbers and variables are evenly-divisible by the root of the number. If the problem was to factor "9x^2-25" you'd know that 9 can evenly be factored by a ratio, along with x^2 and 25.
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    Look the first portion of the problem. Write down what the square root of each item in the problem is. According to the example problem above, the term 9x^2 can be factored into 3x on both sides since the square root of 9 is 3, and the square root of a squared number will become the number itself.
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    Keep the same symbol for this side of the problem.
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    Factor the second portion of the problem after the initial questions problem (the 25 from the example above). Since the square-root of 25 is 5, you may right down the number to the right of your "3x-" portion on your paper.
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    Take your problem and replicate both outside pieces. You'll need to do a little something different for the second portion of the solution as factoring one of these won't be equal on both sides when cross-checking the answer, substituting these in and distributing.
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    Change and write the opposite sign to the second portion of the solution's other factor. Thereby, this operand should then be an addition sign.
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    Look at your final solution. Your final solution, if the problem above was your question" should look something like this:" "(3x-5)(3x+5)"

Tips

  • Cross check your final solution to see if you can arrive at the intended problem again. Use the FOIL method to cross-check.
  • Even if the number isn't a perfect square, it can still be found to be a solvable answer. Just use the square root sign over the initial portion of the answer you'll be given in the problem, and factor the first portion of the problem.
    • The only time when this won't work is when you didn't see the first portion clearly and your answer turns out to be both sides having the square root sign on both sides).

Article Info

Categories: Pages Needing Attention | Algebra