Is #4a^2 − 10a + 25# a perfect square trinomial and how do you factor it?

1 Answer
Jun 11, 2015

Answer:

#4a^2-10a+25# is a perfect square trinomial with factors #(2a-5)^2#

Explanation:

Since a perfect square trinomial has the form
#color(white)("XXXX")##(p+q)^2 = p^2+2pq+q^2#

If #4a^2-10a+25# is to be a perfect square
#color(white)("XXXX")##p^2 = 4a^2 rarr p =+-2a#
and
#color(white)("XXXX")##q^2 = 25 rarr q = +-5#

Picking #p=2a# and #q=-5#
results in a middle term of #-10a#
as required to be a perfect square.