Brief Explanation of the Trinity

Give your best explanation of the Trinity, using specific
texts to support your answer.

I am not sure I am prepared to answer
this.  I believe the basics of the
Trinity include Three Persons, all God, holding distinct offices and
responsibilities, with subordination among Them under Father, yet none of Them
no less God Supreme.  Some texts illustrating
the Three existing simultaneously, yet in Their own roles, would be:

God Holy Spirit, Gen 1.2 “And the
Spirit of God was hovering over the face of the waters“; God Father, Gen 1.26
“Then God said, “Let Us make man in Our image” (plural) and God Jesus, v27 “So
God created man in His own image” (unified), supported by Colossians
1.15-16 “He (Jesus) is the image of the invisible God, the firstborn over all
creation. ¹⁶ For by Him all things were created that are in heaven
and that are on earth, visible and invisible, whether thrones or dominions or
principalities or powers. All things were created through Him and for Him.”

We also see all Three present at Jesus’
baptism in Luke 3.21-22 “²¹ When all the people were baptized, it
came to pass that Jesus also was baptized; and while He prayed, the heaven was
opened. ²² And the Holy Spirit descended in bodily form like a dove
upon Him, and a voice came from heaven which said, “You are My beloved Son; in
You I am well pleased.”