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6 January, 20:25

Which of the following does not factor as a perfect square trinomial? A. 16a^2-72a+81 B. 169x^2+26xy+y^2 C. x^2-18x-81 D. 4x^2+4x+1

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  1. 6 January, 23:37
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    The correct option is C.

    Step-by-step explanation:

    Lets solve each option one by one

    A) 16a^2-72a+81

    According to whole square formula:

    a²-2ab+b² = (a-b) ²

    We have to take the square root of first and third term of each equation.

    a² shows the first term = 16a^2

    The square root of 16a^2 is 4a ... because 4 is the number which can be multiplied two times to give 16 and when we multiply a two times it gives us a².

    b² shows the third term = 81

    The perfect square of 81 is 9.

    2ab shows the middle term.

    2ab = 2 (4a) (9) = 72a

    Thus we can factor it as a perfect square trinomial:

    a²-2ab+b² = (a-b) ²

    16a²-72a+81 = (4a-9) ²

    B) 169x^2+26xy+y^2

    a²+2ab+b² = (a+b) ²

    The square root of 169x² is 13x

    Square root of y² is y

    The middle term 26xy = 2ab = 2 (13x) (y) = 26xy

    Thus we can factor it as a perfect square trinomial:

    a²+2ab+b² = (a+b) ²

    169x^2+26xy+y^2 = (13x+y) ²

    C) x^2-18x-81

    We can not factor it as a perfect square trinomial because the third term is negative.

    D) 4x^2+4x+1

    a²+2ab+b² = (a+b) ²

    The square root of 4x² is 2x

    Square root of 1 is 1

    The middle term 4x=2ab=2 (2x) (1) = 4x

    Thus we can factor it as a perfect square trinomial:

    a²+2ab+b² = (a+b) ²

    4x^2+4x+1 = (2x+1) ²

    Thus the correct option is C ...
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