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