Question

122
course
ap precalculus
due tue, oct 21, 2025
perfect square trinomials
default gallery

1. 4z² - 4z + 1

text math set matrix
answer

Explanation:

Step1: Recall the formula for perfect - square trinomial

The formula for a perfect - square trinomial is \(a^{2}-2ab + b^{2}=(a - b)^{2}\).

Step2: Identify \(a\) and \(b\) in the given trinomial \(4z^{2}-4z + 1\)

For \(4z^{2}-4z + 1\), we have \(a^{2}=4z^{2}\), so \(a = 2z\) (since \((2z)^{2}=4z^{2}\)), and \(b^{2}=1\), so \(b = 1\) (since \(1^{2}=1\)). Also, \(2ab=2\times(2z)\times1 = 4z\).

Step3: Factor the trinomial

Using the formula \(a^{2}-2ab + b^{2}=(a - b)^{2}\), substituting \(a = 2z\) and \(b = 1\), we get \(4z^{2}-4z + 1=(2z - 1)^{2}\).

Answer:

\((2z - 1)^{2}\)