factorise the following perfect square 16X^2-16x+4

To factorize the given expression \(16x^2 - 16x + 4\), we can follow these steps:

### Step 1: Recognize the form
Notice that the expression is a quadratic in the form of \( ax^2 + bx + c \). In this case:
- \( a = 16 \)
- \( b = -16 \)
- \( c = 4 \)

### Step 2: Identify the perfect square trinomial
The expression appears to be a perfect square trinomial. A perfect square trinomial can be written in the form:
\[
(a \cdot x + b)^2 = a^2 \cdot x^2 + 2ab \cdot x + b^2
\]
Here, we need to check if the given expression matches this form.

### Step 3: Write the expression as a perfect square
Compare the given expression \(16x^2 - 16x + 4\) to the expanded form of a binomial square:
\[
(4x - 2)^2 = (4x)^2 - 2 \times 4x \times 2 + 2^2 = 16x^2 - 16x + 4
\]
Thus, the given expression can be factorized as:
\[
(4x - 2)^2
\]

### Final Answer:
\[
16x^2 - 16x + 4 = (4x - 2)^2
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you determine if a quadratic expression is a perfect square trinomial?
2. What is the general formula for expanding a binomial square?
3. How can you factorize non-perfect square trinomials?
4. What is the difference between factorizing and simplifying an expression?
5. How would you factorize \(25x^2 - 30x + 9\)?

### Tip:
Always look for common factors first when trying to factorize a quadratic expression. This can simplify the process and help you identify perfect squares or other factorization methods.

Learn how to factorize the perfect square 16x^2 - 16x + 4 with a step-by-step solution. This problem covers key algebraic concepts, including perfect square trinomials and binomial square formulas. Suitable for high school students in Grades 9-12.

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