Question

How do you factor the expression `9x^2 - 30x +25`?

Answer 1

`9x^2-30x+25 = (3x-5)^2`

Explanation:

This is a perfect square trinomial.

In general `(a+-b)^2 = a^2+-2ab+b^2`

Notice that both `9x^2 = (3x)^2` and `25 = 5^2` are perfect squares, so the only question is whether the middle term matches when you square `(3x-5)`, the minus sign being chosen to at result in a negative coefficient for the middle term.

`(3x-5)^2 = (3x)^2-2(3x)(5)+5^2 = 9x^2-30x+25`