Final answer:
Perfect square trinomials are the expressions where the square root of the first term and the third term are whole numbers, and twice their product equals the middle term. From the expressions given, a. y^(2)+18y+81 and d. y^(2)+20y+100 are perfect square trinomials.
Step-by-step explanation:
In Mathematics, a perfect square trinomial is a special form of trinomial, which is the square of a binomial. To determine whether a trinomial is a perfect square, the following condition should be met: the square root of the first term and the third term are whole numbers, and twice their product equals the middle term.
Let's apply this to each of the given trinomials:
a. y^(2)+18y+81 - The square root of y^2 is y, square root of 81 is 9, and twice their product (2*9y) is 18y, so this is a perfect square trinomial.
b. y^(2)+6y+36 - The square root of y^2 is y, square root of 36 is 6, and twice their product (2*6y) is 12y, so this is not a perfect square trinomial.
c. y^(2)+25y+200 - The square root of y^2 is y, square root of 200 is not a whole number, so this is not a perfect square trinomial.
d. y^(2)+20y+100 - The square root of y^2 is y, square root of 100 is 10, and twice their product (2*10y) is 20y, so this is a perfect square trinomial.
So, the perfect square trinomials are a. y^(2)+18y+81 and d. y^(2)+20y+100.
Learn more about Perfect Square Trinomials