Answer:
Option A and B are perfect square trinomial.
(3x – 5)(3x – 5)
(3x – 5)(5 – 3x)
Step-by-step explanation:
Given the options of trinomials
we have to select the option which will result in a perfect square trinomial.
By algebraic identities
[tex](a+b)(a+b)=(a+b)^2[/tex]
[tex](a+b)(a-b)=a^2-b^2[/tex]
[tex]Option A:(3x-5)(3x-5)[/tex]
[tex](3x-5)(3x-5)=(3x-5)^2[/tex]
which is a perfect square trinomial
[tex]Option B:(3x-5)(5-3x)[/tex]
[tex](3x-5)(5-3x)=(3x-5)(-(3x-5))=-(3x-5)^2[/tex]
which is a perfect square trinomial
[tex]Option C:(3x-5)(3x+5)[/tex]
[tex](3x-5)(3x+5)=(3x)^2-5^2=9x^2-25[/tex]
which is not a perfect square trinomial
[tex]Option D:(3x-5)(-3x-5)[/tex]
[tex](3x-5)(-3x-5)=(3x-5)(-(3x+5))=-(9x^2-25)[/tex]
which is not a perfect square trinomial
Hence, Option A and B are perfect square trinomial.
