Factor the following trinomial.
\[
36 x^{2}-72 x+36
\]

Answer

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Answer

The factored form of the trinomial \(36 x^{2}-72 x+36\) is \(\boxed{36(x - 1)^{2}}\).

Steps

Step 1 ：The given trinomial is a quadratic equation of the form \(ax^2 + bx + c\).

Step 2 ：To factorize it, we can use the formula for factoring a perfect square trinomial, which is \(a^2 - 2ab + b^2 = (a - b)^2\).

Step 3 ：Here, we can see that \(a = 6x\), \(b = 6\), and the trinomial is a perfect square.

Step 4 ：So, we can factorize it as \((6x - 6)^2\).

Step 5 ：The factored form of the trinomial \(36 x^{2}-72 x+36\) is \(\boxed{36(x - 1)^{2}}\).