Ask AI: factor 4x²-4x+1

Sure, I'd be happy to help you factor the quadratic expression \(4x^2 - 4x + 1\). First, let's try to recognize it as a perfect square trinomial. A perfect square trinomial takes the form \((ax + b)^2\), which expands to \(a^2x^2 + 2abx + b^2\). Let's compare the given expression \(4x^2 - 4x + 1\) to this form: - The first term \(4x^2\) is a perfect square: \((2x)^2\). - The last term \(1\) is a perfect square: \(1^2\). - The middle term \(-4x\) should be twice the product of the square roots of the first and last terms: \(2 \cdot 2x \cdot 1 = 4x\). The middle term has a negative sign which fits because \(2 \cdot (2x) \cdot (-1) = -4x\). So, it looks like the expression \(4x^2 - 4x + 1\) fits the form \((ax + b)^2\) where \(a = 2\) and \(b = -1\). Therefore, the expression can be written as: \[ (2x - 1)^2 \] So, the factored form of \(4x^2 - 4x + 1\) is: \[ (2x - 1)^2 \] Please let me know if you need further assistance!