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Chapter 0: Problem 55

Factor each perfect square trinomial. $$9 x^{2}-6 x+1$$

Short Answer

Expert verified
The factored form of the trinomial \(9x^{2}-6x+1\) is \((3x-1)^{2}\)

Step by step solution

01

Identifying 'a' and 'b'

First, recognize that the trinomial \(9x^{2} -6x +1\) has the form \(a^{2}-2ab+b^{2}\). Here, \(a^2\) is \(9x^2\), so 'a' is \(3x\). And \(b^{2}\) is \(1\), so 'b' is \(1\).
02

Factoring the trinomial

After identifying 'a' and 'b', we simply substitute them into the formula \((a - b)^2\). So, \(9x^{2}-6x+1\) becomes \((3x-1)^{2}\).

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