Question

does a^2b^2-12ab+36 is a perfect square trinomial?​

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{a^2b^2-12\,ab+36}$

$\underline{\textsf{To find:}}$

$\textsf{whether the given polynomial is a perfect square trinomial or not}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{a^2b^2-12\,ab+36}$

$\mathsf{=(ab)^2-12\,ab+36}$

$\mathsf{=(ab)^2-6\,ab-6\,ab+36}$

$\mathsf{=ab(ab-6)-6(ab-6)}$

$\mathsf{=(ab-6)(ab-6)}$

$\mathsf{=(ab-6)^2}\;\textsf{is a pefect square}$

$\textsf{Since the given polynomial containing three terms,}$

$\textsf{So it is perfect square trinomial}$

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