Which of the following is a perfect square trinomial?
a. 25x2 + 30xy - 9y2
b. 25x2 - 30xy + 9y2
c. 25x2 - 16xy + 9y2
d. 25x2 + 16xy - 9y2

Whenever you factor a trinomial ax²+bx+c, you find two numbers that add up to b and multiply to get ac, and split bx into those values. Then factor.
With a perfect square trinomial, these values will always be the same and thus you can check by splitting it in half.

25x² + 15xy + 15xy - 9y²
5x(5x+3y) + 3y(5x-3y)
(5x+3y)(5x-3y)
even though this is factorable by splitting 15 and 15, it is not a PST

25x² - 15xy - 15xy + 9y²
5x(5x-3y) -3y(5x-3y)
(5x-3y)(5x-3y)
(5x-3y)²
PST!

25x² - 8xy - 8xy + 9y²
x(25x-8y)-y(8x-9y)
not a perfect square trinomial

25x² + 8xy + 8xy + 9y²
x(25x+y)+y(8x+y)
not a perfect square trinomial

Ans: B. 25x² - 30xy + 9y²