Factorise `25x^(2) - 30xy + 9y^(2)`.
The following steps are involved in solving the above problem . Arrange them in sequential order .
(A) `(5x - 3y)^(2) " " [ because a^(2) - 2b + b^(2) = (a-b)^(2)]`
(B) `(5x)^(2) - 30xy + (3y)^(2) = (5x)^(2) - 2(5x)(3y) + (3y)^(2)`
(C) `(5x - 3y) (5x - 3y)`

Options

A. ABC
B. BCA
C. ACB
D. BAC

Explanation

To factorise the expression \(25x^2 - 30xy + 9y^2\), we can follow these steps:

### Step 1: Identify the perfect square trinomial
We start by recognizing that the expression can be related to the perfect square trinomial form \(a^2 - 2ab + b^2\).

- Here, \(a = 5x\) and \(b = 3y\).
- Therefore, we can rewrite the expression as:
\[ (5x)^2 - 2(5x)(3y) + (3y)^2 \]

### Step 2: Write the expression in the perfect square form
Now we can express the trinomial in the form of a square:
\[ (5x - 3y)^2 \]

### Step 3: Write the final factorised form
Thus, the factorisation of the expression \(25x^2 - 30xy + 9y^2\) is:
\[ (5x - 3y)(5x - 3y) \quad \text{or simply} \quad (5x - 3y)^2 \]

### Summary of Steps
1. Recognize the expression as a perfect square trinomial.
2. Rewrite it in the form \((a - b)^2\).
3. Conclude with the factorised form.