Factorise 25y2−30y+9 completely.

Sure, let's factorise the given quadratic equation step by step.

The given equation is 25y^2 - 30y + 9.

Step 1: Identify a, b, and c in the quadratic equation ax^2 + bx + c. Here, a = 25, b = -30, and c = 9.

Step 2: Check if the equation can be written in the form of (ay + b)^2. For this, b^2 - 4ac should be equal to 0.

Let's check:

(-30)^2 - 4259 = 900 - 900 = 0

Since b^2 - 4ac = 0, the equation can be written in the form of (ay + b)^2.

Step 3: Write the equation in the form of (ay + b)^2.

The equation becomes (5y - 3)^2.

So, the factorised form of 25y^2 - 30y + 9 is (5y - 3)^2.