How do you factor this Binomial?

Question

36t^2 - 18tq + 9q^2

I don't know how to help my sister with her math homework.

Answer 1

You have done some mistake while copying the problem.Please check it up.It may be 36l^2-36lq+9q^2 or something else.However I am doing ipresuming it to be 36l^2-36lq+9q^2

given exp.=9(4l^2-4lq+q^2)
=9{2l)^2-2.2l.q+(q)^2}
=9(2l-q)^2
The answer may also be written as {3(2l-q)}^2 or (6l-3q)^2

Answer 2

Looking at it, the first thing I notice is the coefficients:
36, 18, 9

They are all multiples of 9. So let's divide those out first:

9(4t^2 - 2tq + q^2)

Hm, I was looking to factor it more than that, but it either can't be done or I'm just unable to figure it out right now.

btw, it's not a binomial; it's a trinomial.

Answer 3

First take out the common factor from all the terms:
9(4t^2 -2tq + q²).
Can you factor the term in brackets?
To answer this compute the discriminant, b²-4ac.
It is 4-16 < 0, so the answer is "no".