Question

Which trinomial is a perfect square trinomial?

(A) y2+6y+36

(B) y2+25y+200

(C) y2+18y+81

(D) y2+36y+60

Answer 1

C

Explanation:

think in general

(y + c)² = y² + 2cy + c²

only A and C have a square number as constant term (36 and 81).

and while it is possible to have any real number as c, but the 2cy part needs to fit to the c² part.

6y = 2cy

2c = 6

c = 3

but 3² is 9 and not 36. so, no fit.

25y = 2cy

2c = 25

c = 12.5

but 12.5² is 156.25 and not 200. so, no fit.

18y = 2cy

2c = 18

c = 9

and 9² is indeed 81. so, this fits.

36y = 2cy

2c = 36

c = 18

but 18² is 324 and not 60. so, no fit.

so, only C is a correct answer.