Problem 55 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

The factored form of \(9 x^{2}-6 x+1\) is \((3x-1)^2\).

Step 1 Identify the Trinomial as Perfect Square

Check if the given trinomial \(9 x^{2}-6 x+1\) fits the formula \(a^{2}-2ab+b^{2}\). In this case, \(a=3x\), \(b=1\) since \(3x^{2} = 9x^{2}\), \(2*3x*1 = 6x\) and \(1^{2} = 1\). As the trinomial fits the formula, we can be sure that it is a perfect square trinomial.

Step 2 Write it as Perfect Square

Since the trinomial fits the perfect square trinomial formula \(a^{2}-2ab+b^{2}\), it can be written as \((a-b)^2\). Therefore, we can write \(9 x^{2}-6 x+1\) as \((3x-1)^2\).

Step 3 Factor

The final step to factor the perfect square is to rewrite the equation based on your work in step 2. For this problem, the factored form of \(9 x^{2}-6 x+1\) is \((3x-1)^2\).