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24 March, 15:27

What type of binomial will result in a difference of squares

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  1. 24 March, 15:33
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    If you have a binomial where both terms are a perfect square, you can factor it using difference of squares.

    This also works when you have a number plus another number.

    I'll provide two examples:

    (x^2 - 9)

    The difference of squares states: (a^2 - b^2) = (a + b) (a - b)

    In this case, (x^2 - 9) = (x + 3) (x - 3)

    We can also apply the difference of squares with a number plus another.

    (x^2 + 25)

    We can rewrite this binomial as: (x^2 - (-25))

    Now, we can apply the same steps to factor.

    (x^2 - (-25)) = (x + (√-25)) (x - (√-25))

    Because we have √-25, we can simplify it by multiplying it by i, which will remove the negative.

    This leaves us with (x + 5i) (x - 5i), which is the factored form of x^2 + 25.

    We can verify this by using FOIL.

    x^2 - 5ix + 5ix - 25i^2

    x^2 + 25i^2

    i^2 can be interpreted as - 1, and so we can change the + to -

    x^2 - 25
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