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Question

# Which expression is a perfect-square trinomial?A $9 x^2+49$B $64 x^2-100$C $6 x^2+48 x-96$D $49 x^2-28 x+4$

Solution

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A perfect square trinomial has the first and third terms are perfect squares, and the middle term is twice the product of the square roots of the first and third terms.

Now test each choice: For choices $\textcolor{#c34632}{A}$ and $\textcolor{#c34632}{B}$ there are only two terms. For choice $\textcolor{#c34632}{C}$ there are three terms, but first and third terms are not perfect squares. For choice $\textcolor{#c34632}{D}$ there are three terms, first and third terms are perfect squares, and the middle term is twice the product of the square roots of the first and third terms. Therefore this is the correct choice.

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