Factorise the following expression: 𝑞2−4𝑞+4q 2 −4q+4

The expression you provided seems to have a typo. I believe you meant to write 𝑞^2−4𝑞+4.

Here are the steps to factorise the expression 𝑞^2−4𝑞+4:

1. Identify the coefficients of the quadratic equation. In this case, a = 1 (coefficient of 𝑞^2), b = -4 (coefficient of 𝑞), and c = 4 (constant term).

2. The quadratic equation is in the form of ax^2 + bx + c. We can factorise this into two binomial expressions if the equation is a perfect square trinomial. A perfect square trinomial is in the form of (ax)^2 + 2abx + b^2.

3. Check if the given equation is a perfect square trinomial. We can do this by checking if b^2 = 4ac. In this case, (-4)^2 = 414, which is not true. Therefore, the given equation cannot be factorised using integer coefficients.

4. If the equation was factorisable, we would write it in the form of (ax + b)^2. However, since it is not, the equation remains as 𝑞^2−4𝑞+4.