A perfect square trinomial can be recognized in the following manner:

a2 ± 2ab + b2

1) Check to see if the first and last terms are positive perfect squares.

2) Check to see if the middle term is twice (2 x) the factors (or square roots) of the first and last

terms.

3) If both conditions are met, the factoring is a binomial squared: (a ± b)2

EXAMPLE: #1 25x2 + 30x + 9

25x2 and 9 are both positive perfect squares

30x is 2(5x)(3)

HENCE THE FACTORS ARE: (5x + 3)(5x + 3) or (5x + 3)2

NOTE: since the sign of the second term in the trinomial is positive, the sign in the binomial is positive.

#2 16y2 - 40y + 25

16y2 and 25 are positive perfect squares

40y is 2(4y)(5)

HENCE THE FACTORS ARE: (4y - 5)(4y - 5) or (4y - 5)2

NOTE: since the sign of the second term in the trinomial is negative, the sign in the binomial is negative.