Question

factor the following polynomial.\\(4x^2 - 4x + 1\\)\\((\boxed{?}x - \boxed{})^2\\)

Explanation:

Step1: Recall the perfect square trinomial formula

The perfect square trinomial formula is \(a^{2}-2ab + b^{2}=(a - b)^{2}\). For the polynomial \(4x^{2}-4x + 1\), we can rewrite \(4x^{2}\) as \((2x)^{2}\) and \(1\) as \(1^{2}\), and \(- 4x\) as \(-2\times(2x)\times1\).

Step2: Apply the perfect square trinomial formula

Comparing \(4x^{2}-4x + 1=(2x)^{2}-2\times(2x)\times1+1^{2}\) with \(a^{2}-2ab + b^{2}\), we have \(a = 2x\) and \(b = 1\). So, by the perfect square trinomial formula, \(4x^{2}-4x + 1=(2x - 1)^{2}\).

Answer:

The first box is \(2\) and the second box is \(1\), so the factored form is \((2x - 1)^{2}\)