Which of the following expressions are perfect square trinomials?

Question

Please help:[

16x^2-8x+1

y^2-1


4x^2+44x+121


4x^2-10x+25

x^2-2x+1

y^2-4

4x^2-16x+25

9y^2+60y+100

Answer 1

perfect square trinomials are like (x-y)²

16x²-8x+1, this is the same as (4x-1)², so yes this is a perfect square trinomial

y²-1= (y-1)(y+1) not a perfect sqaure trinomial

4x²-10+25; not factorable for real numbers

x²-2x+1= (x-1)² yes

y²-4= (y-2)(y+2) no

4x²-16x+25; not factorable for real numbers

9y²+60y+100= (3y+10)² yes

Answer 2

A way to check if expressions are perfect square trinomials is to check if the discriminant, b^2 - 4ac, is equal to 0, for a quadratic equation of the form

ax^2 + bx + c

I'll convert the ones which aren't in that form and have you check for yourself.

y^2 - 1 = (1)y^2 + 0y - 1

y^2 - 4 = (1)y^2 + 0y - 4