Answer:
The perfect square trinomial polynomial
\(4a^2-20a+25\).
Step-by-step explanation:
A. Given \(49x^2-28x+16\)
\((7x)^2-2\times 7x\times2+(2)^2+16-4\)
\((7x-2)^2+12\)
It is not of the perfect square form \((a-b)^2 or (a+b)^2\).
Therefore, the polynomial is not a perfect square trinomial polynomial.Hence, option A is false.
B.\(4a^2-20a+25\)
\((2a)^2-2\times 2a\times 5+(5)^2\)
\((2a-5)^2\)
It is a perfect square trinomial polynomial because it is of the perfect square form \((a-b)^2\) hence, It is perfect square polynomial and the polynomial have three terms therefore, it is trinomial.Hence, option B is true.
C.\(25b^2-20b-16\)
\((5b)^2-2\times 5b\times 2+(2)^2-4-16\)
\((5b-2)^2-20\)
It is not of the perfect square form \((a-b)^2\).Hence, option C is false.
D.\(16x^2-24x-9\)
\((4x)^2-2\times 4x\times 3+9-9-9\)
\((4x-3)^2-18\)
It is not of the perfecr square form \((a-b)^2\). Hence, the option D is false.
