Factorise:
`p ^(2)- 10 p + 25`

Answer

To factorise the expression \( p^2 - 10p + 25 \), we can follow these steps:

### Step 1: Identify the quadratic expression
The given expression is:
\[ p^2 - 10p + 25 \]

### Step 2: Recognize the form of a perfect square
We need to check if this expression can be expressed as a perfect square trinomial. A perfect square trinomial takes the form:
\[ (a - b)^2 = a^2 - 2ab + b^2 \]
where \( a^2 \) is the square of the first term, \( b^2 \) is the square of the second term, and \( -2ab \) is the middle term.

### Step 3: Identify \( a \) and \( b \)
In our expression:
- The first term \( p^2 \) suggests that \( a = p \).
- The last term \( 25 \) suggests that \( b^2 = 25 \), which means \( b = 5 \).

### Step 4: Check the middle term
Now, we check the middle term:
\[ -2ab = -2(p)(5) = -10p \]
This matches the middle term of our expression, which is \(-10p\).

### Step 5: Write the expression as a perfect square
Since we have confirmed that the expression fits the form of a perfect square, we can write:
\[ p^2 - 10p + 25 = (p - 5)^2 \]

### Final Answer
Thus, the factorised form of the expression \( p^2 - 10p + 25 \) is:
\[ (p - 5)^2 \]

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