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How do you factor the difference of two squares? How do you factor the perfect square trinomial? How do you factor the sum and difference of two cubes? Which of these three makes the most sense to you? Explain why.

  • algebra -

    Difference of two squares:
    Example: x^2 - 9 factors to (x+3)(x-3)

    Perfect squares:

    x^2 + 6x + 9 = (x+3)(x+3)
    x^2 -6x + 9 = (x-3)(x-3)


    x^3 - 27 factors to
    (x-3)(x^2 +3x +9)

    x^3 + 27 factors to
    (x+3)(x^2 -3x +9)

    Can you see the pattern?

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