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Identify the expression inside the square root.

Biology

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Answer

|x-2|

Step-by-step solution

4 steps

  1. Identify the expression inside the square root.

    The expression inside the square root is x2−4x+4x^2 - 4x + 4.

  2. Factor the quadratic trinomial.

    This is a perfect square trinomial, which follows the pattern (A−B)2=A2−2AB+B2(A-B)^2 = A^2 - 2AB + B^2.
    Here, A2=x2A^2 = x^2, so A=xA=x.
    And B2=4B^2 = 4, so B=2B=2.
    Check the middle term: −2AB=−2(x)(2)=−4x-2AB = -2(x)(2) = -4x, which matches the given expression.
    So, x2−4x+4=(x−2)2x^2 - 4x + 4 = (x-2)^2.

  3. Substitute the factored form back into the square root.

    x2−4x+4=(x−2)2\sqrt{x^2 - 4x + 4} = \sqrt{(x-2)^2}

  4. Simplify the square root.

    The square root of a squared term is the absolute value of that term.

    (x−2)2=∣x−2∣\sqrt{(x-2)^2} = |x-2|

    The simplified expression is:

    ∣x−2∣\boxed{|x-2|}

    Just one more to go today! Send it over.

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