Question

Which trinomial is a perfect square trinomial? y2 + 6y + 36 y2 + 18y + 81 y2 + 50y + 100 y2 + 25y + 200

Answer 1

To determine a perfect square trinomial, check if the first and last terms are perfect squares, and if the middle term is twice the product of the square roots of the first and last terms.

Step-by-step explanation:

A perfect square trinomial is a trinomial expression that can be factored into a square of a binomial. To determine which trinomial is a perfect square trinomial, we need to check if the first and last terms are perfect squares, and if the middle term is twice the product of the square roots of the first and last terms.

Let's apply this to each trinomial:

y2 + 6y + 36: The first term y2 is a perfect square, the last term 36 is a perfect square, and the middle term 6y is twice the product of the square roots of y2 and 36. Therefore, this trinomial is a perfect square trinomial.

y2 + 18y + 81: This trinomial satisfies all the conditions for a perfect square trinomial, as the first term y2, last term 81, and middle term 18y are all perfect squares and the middle term is twice the product of the square roots.

y2 + 50y + 100: The first term y2 is a perfect square, the last term 100 is a perfect square, but the middle term 50y is not twice the product of the square roots, so this trinomial is not a perfect square trinomial.

y2 + 25y + 200 :The middle term 25y is not twice the product of the square roots, so this trinomial is not a perfect square trinomial.

Answer 2

Out of the four trinomials, y^2+18y+81 is correct.
Step By Step Answer:
To determine a perfect square trinomial, the first and third terms have to be square roots and the middle term has to be two times the square root of the third term.

y^2 is a square root and 81 is a square root.
y^2 simplifies to y and 81 simplifies to 9.
It would be y+18y+9
The third term is 9, so multiply that by two and you get 18!
Therefore, that is correct!
y^2+18y+81 is a perfect square trinomial!

Hope this helps!