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Factorize the expression x2 - 9.

Mathematics

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Answer

d

a. (x+3)(x−3)\text{a. } (x+3)(x-3)

Step-by-step solution

2 steps

To factorize the expression x2−9x^2 - 9, we recognize it as a difference of squares. The general formula for a difference of squares is a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b).

  1. Identify aa and bb in the expression.

    In x2−9x^2 - 9, we have a2=x2a^2 = x^2, so a=xa = x.
    We also have b2=9b^2 = 9, so b=9=3b = \sqrt{9} = 3.

  2. Apply the difference of squares formula.

    Substitute a=xa=x and b=3b=3 into the formula (a−b)(a+b)(a - b)(a + b).

    x2−9=(x−3)(x+3)x^2 - 9 = (x - 3)(x + 3)

    Comparing this with the given options:
    a. (x+3)(x−3)(x+3)(x-3)
    b. (x−1)(x−9)(x-1)(x-9)
    c. (x−3)(x−3)(x-3)(x-3)
    d. (x+9)(x−1)(x+9)(x-1)

    Option a is equivalent to our result, as the order of multiplication does not change the product.

    The final answer is a. (x+3)(x−3)\boxed{\text{a. } (x+3)(x-3)}.

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