Fractorise the
`4x ^(2) - 20 x + 25`

Answer

To factorize the expression \(4x^2 - 20x + 25\), we can follow these steps:

### Step 1: Identify the coefficients
The given expression is \(4x^2 - 20x + 25\). Here, we can identify:
- \(a = 4\) (coefficient of \(x^2\))
- \(b = -20\) (coefficient of \(x\))
- \(c = 25\) (constant term)

### Step 2: Rewrite the expression
We can rewrite the expression in a form that allows us to factor it. Notice that \(4x^2\) can be expressed as \((2x)^2\) and \(25\) can be expressed as \(5^2\). Thus, we can rewrite the expression as:
\[ (2x)^2 - 20x + 5^2 \]

### Step 3: Recognize the pattern
The expression \(4x^2 - 20x + 25\) can be recognized as a perfect square trinomial. The general form of a perfect square trinomial is:
\[ A^2 - 2AB + B^2 = (A - B)^2 \]
In our case:
- \(A = 2x\)
- \(B = 5\)

### Step 4: Apply the perfect square formula
Using the perfect square formula, we can write:
\[ 4x^2 - 20x + 25 = (2x - 5)^2 \]

### Step 5: Write the final factorized form
Thus, the factorized form of the expression is:
\[ (2x - 5)(2x - 5) \quad \text{or} \quad (2x - 5)^2 \]

### Final Answer:
The factorization of \(4x^2 - 20x + 25\) is \((2x - 5)^2\).

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