How do you know if # 9a^2 − 30a + 25# is a perfect square trinomial and how do you factor it?

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Answer 1 · 2015-06-27T21:41:14

Notice that #9a^2 = (3a)^2# and #25 = 5^2#

Need to check that the middle term is #+-2*3a*5 = +-30a# - Yes.

#9a^2-30a+25 = (3a-5)^2#

All perfect square trinomials are of the form:

#A^2+-2AB+B^2 = (A+-B)^2#

In our example, we can recognise #A=3a# and #B=5#, so just need to check that the middle term is correct.

#2AB = 2 xx 3a xx 5 = 30a#

So we have #A^2-2AB+B^2 = (A-B)^2 = (3a-5)^2#