Answer:
D. 4x^2 + 20x + 25
Explanation:
The square of a binomial is ...
(a +b)² = a² +2ab +b²
Application
The trinomial will be a perfect square if the linear term is twice the product of the square roots of the other two terms.
A. √(36x^2) = 6x; √16 = 4; double the product is 2(6x)(4) = 48x, not 4x
B. √(16x^2) = 4x; √36 = 6; double the product is 2(4x)(6) = 48x, not 8x
C. √(25x^2) = 5x; √4 = 2; double the product is 2(5x)(2) = 20x, not 9x
D. √(4x^2) = 2x; √25 = 5; double the product is 2(2x)(5) = 20x, a match
The perfect square trinomial is 4x² +20x +25.
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Additional comment
The square (a -b)² is a² -2ab +b². That is, the sign of the linear term is the sign of the binomial. The square roots can be positive or negative, so the same logic as above can be used to determine if the magnitude of the linear term is correct.
Strictly speaking, the middle term is "linear" only if one of 'a' or 'b' is linear (first degree in one variable).