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a perfect square trinomial has a factor that is identical to the other factor. In this case, from the first term, the factor is composed of 2x while from the third term, there is a term 7 involved. In this case, the factor is 2x + 7. so the second term has to be 2(27) equal to 28

Answer:

The perfect square trinomial is given by:

                   \(4x^2+28x+49\)

Step-by-step explanation:

We are given a expression as follows:

              \(4x^2+-----x+49\)

we know that a perfect square trinomial is of the form:

\((ax)^2+2abx+b^2\)

Here we could represent our given expression as:

\(4x^2+-----x+49=(2x)^2+-----x+7^2\)

i.e.

a=2 , b=7

Hence, we have:

\(2ab=2\times 2\times 7\\\\2ab=28\)

Hence, the perfect square trinomial is:

                  \(4x^2+28x+49\)

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