Question

Which will result in a perfect square trinomial?

Answer 1

(3x-5)(3x-5)
Because it's (3x-5)²=9x²-30x+25

Answer 2

Answer: (3x-5)(3x-5)

Explanation:

A perfect square trinomial is a polynomial that can be expressed in the form of the square of binomial.

Or that is a square root of a binomial.

`(3x-5)(3x-5)= (3x-5)^2`

where 3x - 5 is a bionomial,

⇒ (3x-5)(3x-5) is a perfect square trinomial,

`(3x-5)(5-3x) = -(3x-5)(3x-5)=-(3x-5)^2`

But,
`-(3x-5)^2` is not a perfect square root of a binomial,

⇒ (3x-5)(5-3x) is not a perfect square trinomial,

`(3x-5)(3x+5) = (3x)^2-(5)^2=9x^2-25`

But,
`9x^2-25` is not a perfect square root of a binomial,

⇒ (3x-5)(3x+5) is not a perfect square trinomial,

`(3x-5)(-3x-5)=-(3x-5)(3x+5) = -[(3x)^2-(5)^2]=-9x^2+25`

But,
`-9x^2+25` is not a perfect square root of a binomial,

⇒ (3x-5)(-3x-5) is not a perfect square trinomial,