Question

1. factor the perfect square trinomial

x² - 18x + 81.
a (x - 9)²
b (x - 9)(x + 9)
c (x + 9)²
d (x - 18)²

Explanation:

Step1: Recall perfect square formula

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

Step2: Identify \(a\) and \(b\)

For \(x^2-18x + 81\), we have \(a = x\) (since \(a^2=x^2\)), and \(2ab = 18x\). Substituting \(a=x\) into \(2ab = 18x\), we get \(2\times x\times b=18x\), so \(b = 9\) (because \(2xb = 18x\) implies \(b = 9\) after dividing both sides by \(2x\)). Also, \(b^2=9^2 = 81\), which matches the constant term.

Step3: Apply the formula

Using the formula \(a^2-2ab + b^2=(a - b)^2\) with \(a=x\) and \(b = 9\), we get \(x^2-18x + 81=(x - 9)^2\).

Answer:

A. \((x - 9)^2\)