Question

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

Answer 1

`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.